  We present direct observational evidence for star formation quenching in
galaxy groups in the redshift range 0<z<2.5. We utilize a large sample of
nearly 6000 groups, selected by fixed cumulative number density from three
photometric catalogs, to follow the evolving quiescent fractions of central and
satellite galaxies over roughly 11 Gyr. At z~0, central galaxies in our sample
range in stellar mass from Milky Way/M31 analogs (M=6.5x10^10 M\solar) to
nearby massive ellipticals (M=1.5x10^11 M\solar). Satellite galaxies in the
same groups reach masses as low as twice that of the Large Magellanic Cloud
(M=6.5x10^9 M\solar). Using statistical background subtraction, we measure the
average rest-frame colors of galaxies in our groups and calculate the evolving
quiescent fractions of centrals and satellites over seven redshift bins. Our
analysis shows clear evidence for star formation quenching in group halos, with
a different quenching onset for centrals and their satellite galaxies. Using
halo mass estimates for our central galaxies, we find that star formation shuts
off in centrals when typical halo masses reach between 10^12 and 10^13 M\solar,
consistent with predictions from the halo quenching model. In contrast,
satellite galaxies in the same groups most likely undergo quenching by
environmental processes, whose onset is delayed with respect to their central
galaxy. Although star formation is suppressed in all galaxies over time, the
processes that govern quenching are different for centrals and satellites.
While mass plays an important role in determining the star formation activity
of central galaxies, quenching in satellite galaxies is dominated by the
environment in which they reside.
