  Using a large SDSS galaxy group catalogue, we study how the stellar ages and
metallicities of central and satellite galaxies depend on stellar mass and halo
mass. We find that satellites are older and metal-richer than centrals of the
same stellar mass. In addition, the slopes of the age-stellar mass and
metallicity-stellar mass relations are found to become shallower in denser
environments. This is due to the fact that the average age and metallicity of
low mass satellite galaxies increase with the mass of the halo in which they
reside. A comparison with the semi-analytical model of Wang et al. (2008) shows
that it succesfully reproduces the fact that satellites are older than centrals
of the same stellar mass and that the age difference increases with the halo
mass of the satellite. This is a consequence of strangulation, which leaves the
stellar populations of satellites to evolve passively, while the prolonged star
formation activity of centrals keeps their average ages younger. The resulting
age offset is larger in more massive environments because their satellites were
accreted earlier. The model fails, however, in reproducing the halo mass
dependence of the metallicities of low mass satellites, yields
metallicity-stellar mass and age-stellar mass relations that are too shallow,
and predicts that satellite galaxies have the same metallicities as centrals of
the same stellar mass, in disagreement with the data. We argue that these
discrepancies are likely to indicate the need to (i) modify the recipes of both
supernova feedback and AGN feedback, (ii) use a more realistic description of
strangulation, and (iii) include a proper treatment of the tidal stripping,
heating and destruction of satellite galaxies. [Abridged]
