Is there a theory of induced representations for semigroups? Given a semigroup $G$, a subgroup $H\subseteq G$ (not merely a subsemigroup) and a representation $\rho: H\rightarrow GL(V)$ for some vector space $V$, is there a canonical definition of an induced representation on some vector space $V^\prime$ containing $V$? 
Is there even a well developed representation theory of semigroups? 
If so, please give me references.
(I encountered this question while working on my master's thesis, which includes a generalization/extension of certain Hecke operators on vector valued modular forms.)
Thanks in advance,
mathmax
Edit: Corrected typo; of course, $\rho$ has to be a representation of $H$ not of $G$

I am writing a book on the representation theory of monoids. The latest version is http://www.sci.ccny.cuny.edu/~benjamin/monoidrep.pdf
You will see that there is a more subtle way to induce representations of a monoid from its maximal subgroups than the way suggested by Phil which is essential for constructing the simple modules.  
