We explore how the star formation and metal enrichment histories of present-day galaxies have been affected by environment combining stellar population parameter estimates and group environment characterization for SDSS DR7. We compare stellar ages, stellar metallicities and element abundance ratios [alpha/Fe] of satellite and central galaxies, as a function of their stellar and host group halo mass, controlling for the current star formation rate and for the infall epoch. We confirm that below log(Mstar/Msun)=10.5 satellites are older and metal-richer than equally-massive central galaxies. On the contrary, we do not detect any difference in their [alpha/Fe]: this depends primarily on stellar mass and not on group hierarchy nor host halo mass. We also find that the differences in the median age and metallicity of satellites and centrals at stellar mass below 10^{10.5}Msun are largely due to the higher fraction of passive galaxies among satellites and as a function of halo mass. We argue that the observed trends at low masses reveal the action of satellite-specific environmental effects in a `delayed-then-rapid' fashion. When accounting for the varying quiescent fraction, small residual excess in age, metallicity and [alpha/Fe] emerge for satellites dominated by old stellar populations and residing in halos more massive than 10^{14}Msun, compared to equally-massive central galaxies. This excess in age, metallicity and [alpha/Fe] pertain to ancient infallers, i.e. satellites that have accreted onto the current halo more than 5 Gyr ago. This result points to the action of environment in the early phases of star formation in galaxies located close to cosmic density peaks.