  We use our state-of-the-art Galaxy Evolution and Assembly (GAEA)
semi-analytic model to study how and on which time-scales star formation is
suppressed in satellite galaxies. Our fiducial stellar feedback model,
implementing strong stellar driven outflows, reproduces relatively well the
variations of passive fractions as a function of galaxy stellar mass and halo
mass measured in the local Universe, as well as the `quenching' time-scales
inferred from the data. We show that the same level of agreement can be
obtained by using an alternative stellar feedback scheme featuring lower
ejection rates at high redshift, and modifying the treatment for hot gas
stripping. This scheme over-predicts the number densities of low to
intermediate mass galaxies. In addition, a good agreement with the observed
passive fractions can be obtained only by assuming that cooling can continue on
satellites, at the rate predicted considering halo properties at infall, even
after their parent dark matter substructure is stripped below the resolution of
the simulation. For our fiducial model, the better agreement with the observed
passive fractions can be ascribed to: (i) a larger cold gas fraction of
satellites at the time of accretion, and (ii) a lower rate of gas reheating by
supernovae explosions and stellar winds with respect to previous versions of
our model. Our results suggest that the abundance of passive galaxies with
stellar mass larger than ~10^10 Msun is primarily determined by the
self-regulation between star formation and stellar feedback, with environmental
processes playing a more marginal role.
