user11541: If there is no Self , then what Self is there to be affected by the karma which the non-Self now performs?
EDIT: A similar question I guess was asked in Samyutta Nikaya and Buddha replied as follows :
" With thy thoughts, which are under the dominion of desire, dost thou dream thou canst overhaul the teaching of the Master "
However I not sure what that means. I would be really happy if someone can explain the meaning of that answer from Buddha.

user8044: You and I do exist in the world, so one cannot say there is “no self”. The reason that it is said that there is “no self”, is because no person remains the same. 
It is in the Brahmajala sutta that we find the Buddha's take on this. He explained that both views of “self” and ‘no self” are wrong. This wrong view is one of the 62 types of mica ditthi as explained in the scriptures. 

user11009: What Buddha saying is beings are dependently originated due to ignorance. As far as we have self view we continue to accumulate Sankhara and we continue to exist. Sankhara is not the self but it is the accumulation due to self view.
Beings are effected by kamma due to selfview. Once you eliminate self identificaton (Arahant) there is no more becoming or affected by the kamma.

user11541: After a little research I found the original question in Samyutta Nikaya along with Buddha's response.  

Then what self can those acts affect which are not self-wrought?"
  Thereupon the Exalted One, with his thought reading the thoughts of
  that brother's mind, said to the brethren: It is possible, brethren,
  that some senseless fellow, sunk in ignorance and led astray by
  craving, may think to go beyond the Master's teaching thus: "So then
  you say that body is not the Self; feeling is not the Self, perception
  is not the Self, the activities are not the Self, and consciousness is
  not the Self, Then what self can those acts affect which are not
  self-wrought?" That question, brethren, I have already answered thus
  and thus in those teachings that I have given you. Now what think ye,
  brethren? Is body permanent or impermanent?" "Impermanent, lord."
  "That which is impermanent, is it weal or woe?" "Woe, lord." "But that
  which is impermanent, woeful, unstable in nature, is it right to
  regard it thus: "This is mine, this am I this is the Self of me?"
  "Surely not, lord." Is feeling permanent or impermanent?"
  "Impermanent, lord." "That which is impermanent, is it weal or woe?"
  "Woe, lord." "But that which is impermanent, woeful, unstable in
  nature, is it right to regard it thus: "This is mine, this am I this
  is the Self of me?" "Surely not, lord." Is perception permanent or
  impermanent?" "Impermanent, lord." "That which is impermanent, is it
  weal or woe?" "Woe, lord." "But that which is impermanent, woeful,
  unstable in nature, is it right to regard it thus: "This is mine, this
  am I this is the Self of me?" "Surely not, lord." Are the activities
  permanent or impermanent?" "Impermanent, lord." "That which is
  impermanent, is it weal or woe?" "Woe, lord." "But that which is
  impermanent, woeful, unstable in nature, is it right to regard it
  thus: "This is mine, this am I this is the Self of me?" "Surely not,
  lord." Is consciousness permanent or impermanent?" "Impermanent,
  lord." "That which is impermanent, is it weal or woe?" "Woe, lord."
  "But that which is impermanent, woeful, unstable in nature, is it
  right to regard it thus: "This is mine, this am I this is the Self of
  me?" "Surely not, lord."
      Therefore, brethren, every body whatever, be it past, future or present, be it inward or outward, gross or subtle, low or high, far or
  near, - every body should be thus regarded, as it really is, by right
  insight: "This is not mine. This I am not. This is not the Self of
  me."
Every feeling whatever, be it past, future or present, be it inward or
  outward, gross or subtle, low or high, far or near, - every feeling
  should be thus regarded, as it really is, by right insight: "This is
  not mine. This I am not. This is not the Self of me."
Every perception whatever, be it past, future or present, be it inward
  or outward, gross or subtle, low or high, far or near, - every
  perception should be thus regarded, as it really is, by right insight:
  "This is not mine. This I am not. This is not the Self of me."
Every activity whatever, be it past, future or present, be it inward
  or outward, gross or subtle, low or high, far or near, - every
  activity should be thus regarded, as it really is, by right insight:
  "This is not mine. This I am not. This is not the Self of me."
Every consciousness whatever, be it past, future or present, be it
  inward or outward, gross or subtle, low or high, far or near, - every
  consciousness should be thus regarded, as it really is, by right
  insight: "This is not mine. This I am not. This is not the Self of
  me."
      "Wherefore, brethren, he who thus sees conceives disgust at body, at feeling, at perception, at the activities, at consciousness. Being
  disgusted he is repelled by them; by that repulsion he is released; by
  that release he is set free; knowledge arises: in the freed man is the
  freed thing, and he knows: 'Destroyed is rebirth; lived is the
  righteous life; done is the task; for life in these conditions there
  is no hereafter.'"


user471: This comes from the Acela Sutta (although this quote comes from here). Basically, it's pointless to ask questions like this, according to the Buddha. Instead, we should approach it from the perspective of dependent origination.

Again, when the Buddha was asked by the naked ascetic Kassapa whether
  suffering was of one's own making or of another's or both or neither,
  the Buddha replied "Do not put it like that." When asked whether there
  was no suffering or whether the Buddha neither knew nor saw it, the
  Buddha replied that there was, and that he both knew and saw it. He
  then said "Kassapa, if one asserts that 'He who makes (it) feels (it):
  being one existent from the beginning, his suffering is of his own
  making,' then one arrives at eternalism. But if one asserts that one
  makes (it), another feels (it); being one existent crushed out by
  feeling, his suffering is of another's making,' then one arrives at
  annihilationism. Instead of resorting to either extreme a Tathaagata
  teaches the Dhamma by the middle way (by dependent origination)"
  (S. XII, 17/vol. ii, 20).


11541: <p>If there is no Self , then what Self is there to be affected by the karma which the non-Self now performs?</p>

<p>EDIT: A similar question I guess was asked in Samyutta Nikaya and Buddha replied as follows :
" With thy thoughts, which are under the dominion of desire, dost thou dream thou canst overhaul the teaching of the Master "
However I not sure what that means. I would be really happy if someone can explain the meaning of that answer from Buddha.</p>
 8044: <p>You and I do exist in the world, so one cannot say there is “no self”. The reason that it is said that there is “no self”, is because no person remains the same. 
It is in the Brahmajala sutta that we find the Buddha's take on this. He explained that both views of “self” and ‘no self” are wrong. This wrong view is one of the 62 types of mica ditthi as explained in the scriptures. </p>
 11009: <p>What Buddha saying is beings are dependently originated due to ignorance. As far as we have self view we continue to accumulate Sankhara and we continue to exist. Sankhara is not the self but it is the accumulation due to self view.
Beings are effected by kamma due to selfview. Once you eliminate self identificaton (Arahant) there is no more becoming or affected by the kamma.</p>
 11541: <p>After a little research I found the original question in <a href="http://obo.genaud.net/dhamma-vinaya/pts/sn/03_kv/sn03.22.082.wood.pts.htm" rel="nofollow noreferrer">Samyutta Nikaya</a> along with Buddha's response.  </p>

<blockquote>
  <p>Then what self can those acts affect which are not self-wrought?"
  Thereupon the Exalted One, with his thought reading the thoughts of
  that brother's mind, said to the brethren: It is possible, brethren,
  that some senseless fellow, sunk in ignorance and led astray by
  craving, may think to go beyond the Master's teaching thus: "So then
  you say that body is not the Self; feeling is not the Self, perception
  is not the Self, the activities are not the Self, and consciousness is
  not the Self, Then what self can those acts affect which are not
  self-wrought?" That question, brethren, I have already answered thus
  and thus in those teachings that I have given you. Now what think ye,
  brethren? Is body permanent or impermanent?" "Impermanent, lord."
  "That which is impermanent, is it weal or woe?" "Woe, lord." "But that
  which is impermanent, woeful, unstable in nature, is it right to
  regard it thus: "This is mine, this am I this is the Self of me?"
  "Surely not, lord." Is feeling permanent or impermanent?"
  "Impermanent, lord." "That which is impermanent, is it weal or woe?"
  "Woe, lord." "But that which is impermanent, woeful, unstable in
  nature, is it right to regard it thus: "This is mine, this am I this
  is the Self of me?" "Surely not, lord." Is perception permanent or
  impermanent?" "Impermanent, lord." "That which is impermanent, is it
  weal or woe?" "Woe, lord." "But that which is impermanent, woeful,
  unstable in nature, is it right to regard it thus: "This is mine, this
  am I this is the Self of me?" "Surely not, lord." Are the activities
  permanent or impermanent?" "Impermanent, lord." "That which is
  impermanent, is it weal or woe?" "Woe, lord." "But that which is
  impermanent, woeful, unstable in nature, is it right to regard it
  thus: "This is mine, this am I this is the Self of me?" "Surely not,
  lord." Is consciousness permanent or impermanent?" "Impermanent,
  lord." "That which is impermanent, is it weal or woe?" "Woe, lord."
  "But that which is impermanent, woeful, unstable in nature, is it
  right to regard it thus: "This is mine, this am I this is the Self of
  me?" "Surely not, lord."
      Therefore, brethren, every body whatever, be it past, future or present, be it inward or outward, gross or subtle, low or high, far or
  near, - every body should be thus regarded, as it really is, by right
  insight: "This is not mine. This I am not. This is not the Self of
  me."</p>
  
  <p>Every feeling whatever, be it past, future or present, be it inward or
  outward, gross or subtle, low or high, far or near, - every feeling
  should be thus regarded, as it really is, by right insight: "This is
  not mine. This I am not. This is not the Self of me."</p>
  
  <p>Every perception whatever, be it past, future or present, be it inward
  or outward, gross or subtle, low or high, far or near, - every
  perception should be thus regarded, as it really is, by right insight:
  "This is not mine. This I am not. This is not the Self of me."</p>
  
  <p>Every activity whatever, be it past, future or present, be it inward
  or outward, gross or subtle, low or high, far or near, - every
  activity should be thus regarded, as it really is, by right insight:
  "This is not mine. This I am not. This is not the Self of me."</p>
  
  <p>Every consciousness whatever, be it past, future or present, be it
  inward or outward, gross or subtle, low or high, far or near, - every
  consciousness should be thus regarded, as it really is, by right
  insight: "This is not mine. This I am not. This is not the Self of
  me."
      "Wherefore, brethren, he who thus sees conceives disgust at body, at feeling, at perception, at the activities, at consciousness. Being
  disgusted he is repelled by them; by that repulsion he is released; by
  that release he is set free; knowledge arises: in the freed man is the
  freed thing, and he knows: 'Destroyed is rebirth; lived is the
  righteous life; done is the task; for life in these conditions there
  is no hereafter.'"</p>
</blockquote>
 471: <p>This comes from the <a href="http://www.accesstoinsight.org/tipitaka/sn/sn12/sn12.017.than.html" rel="nofollow noreferrer">Acela Sutta</a> (although this quote comes from <a href="http://www.accesstoinsight.org/lib/authors/various/wheel202.html#theravada" rel="nofollow noreferrer">here</a>). Basically, it's pointless to ask questions like this, according to the Buddha. Instead, we should approach it from the perspective of <a href="https://buddhism.stackexchange.com/q/48/471">dependent origination</a>.</p>

<blockquote>
  <p><strong>Again, when the Buddha was asked by the naked ascetic Kassapa whether
  suffering was of one's own making or of another's or both or neither,
  the Buddha replied "Do not put it like that."</strong> When asked whether there
  was no suffering or whether the Buddha neither knew nor saw it, the
  Buddha replied that there was, and that he both knew and saw it. He
  then said "Kassapa, if one asserts that 'He who makes (it) feels (it):
  being one existent from the beginning, his suffering is of his own
  making,' then one arrives at <strong>eternalism</strong>. But if one asserts that one
  makes (it), another feels (it); being one existent crushed out by
  feeling, his suffering is of another's making,' then one arrives at
  <strong>annihilationism</strong>. Instead of resorting to either extreme a <strong>Tathaagata
  teaches the Dhamma by <a href="https://buddhism.stackexchange.com/a/8164/471">the middle way</a> (by <a href="https://buddhism.stackexchange.com/q/48/471">dependent origination</a>)</strong>"
  (S. XII, 17/vol. ii, 20).</p>
</blockquote>
