Kinematic and stellar population properties of the counter-rotating
  components in the S0 galaxy NGC 1366
  Context. Many disk galaxies host two extended stellar components that rotate
in opposite directions. The analysis of the stellar populations of the
counter-rotating components provides constraints on the environmental and
internal processes that drive their formation.
  Aims. The S0 NGC 1366 in the Fornax cluster is known to host a stellar
component that is kinematically decoupled from the main body of the galaxy.
Here we successfully separated the two counter-rotating stellar components to
independently measure the kinematics and properties of their stellar
populations.
  Methods. We performed a spectroscopic decomposition of the spectrum obtained
along the galaxy major axis and separated the relative contribution of the two
counter-rotating stellar components and of the ionized-gas component. We
measured the line-strength indices of the two counter-rotating stellar
components and modeled each of them with single stellar population models that
account for the {\alpha}/Fe overabundance.
  Results. We found that the counter-rotating stellar component is younger, has
nearly the same metallicity, and is less {\alpha}/Fe enhanced than the
corotating component. Unlike most of the counter-rotating galaxies, the ionized
gas detected in NGC 1366 is neither associated with the counter-rotating
stellar component nor with the main galaxy body. On the contrary, it has a
disordered distribution and a disturbed kinematics with multiple velocity
components observed along the minor axis of the galaxy.
  Conclusions. The different properties of the counter-rotating stellar
components and the kinematic peculiarities of the ionized gas suggest that NGC
1366 is at an intermediate stage of the acquisition process, building the
counter-rotating components with some gas clouds still falling onto the galaxy.
