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.

11 pages, 6 figures, 1 appendix. Accepted for publication in MNRAS