  The properties of dark matter halos, including mass growth, correlate with
larger scale environment at fixed mass, an effect known as assembly bias.
However, whether this environmental dependence manifests itself in galaxy
properties remains unclear. We apply a group-finding algorithm to DR7 of the
SDSS to estimate the halo mass of each galaxy and to decompose galaxies into
those that exist at the centers of distinct halos and those that orbit as
satellites within larger halos. Using the 4000-A break as a measure of star
formation history, we examine the correlation between the quenched fraction of
galaxies, f_q, and large-scale environment, rho. At all galaxy magnitudes,
there is a positive, monotonic relationship between f_q and rho. We use the
group catalog to decompose this correlation into the contribution from central
and satellite galaxies as a function of halo mass. Because satellites are more
likely to be quenched than central galaxies, the observed f_q-rho correlation
is primarily due to variations of the halo mass function with environment,
which causes a larger fraction of satellite galaxies at high rho. For low-mass
central galaxies (Mgal <~ 10^10.0 Msol/h^2), there is no correlation between
f_q and rho. These results are inconsistent with the strong assembly bias of
dark matter halos seen in this mass regime if recent galaxy growth at all
correlates with recent halo growth, as we demonstrate through a high resolution
N-body simulation. We also find that the mean stellar age of quenched central
galaxies is independent of rho at fixed Mgal, while the formation times of low
mass halos vary significantly. We conclude that the processes that halt the
star formation of low mass central galaxies are not correlated to the formation
histories of their host halos, and old galaxies do not reside preferentially in
old halos. (Abridged)
