  Abridged - We quantify the effect of the galaxy group environment (for 12.5 <
log(M_group/Msun) < 14.0) on the star formation rates of the
(morphologically-selected) population of disk-dominated local Universe spiral
galaxies (z < 0.13) with stellar masses log(M*/Msun) > 9.5. Within this
population, we find that, while a small minority of group satellites are
strongly quenched, the group centrals, and the large majority of satellites
exhibit levels of SFR indistinguishable from ungrouped "field" galaxies of the
same M*, albeit with a higher scatter, and for all M*. Modelling these results,
we deduce that disk-dominated satellites continue to be characterized by a
rapid cycling of gas into and out of their ISM at rates similar to those
operating prior to infall, with the on-going fuelling likely sourced from the
group intrahalo medium (IHM) on Mpc scales, rather than from the
circum-galactic medium on 100kpc scales. Consequently, the color-density
relation of the galaxy population as a whole would appear to be primarily due
to a change in the mix of disk- and spheroid-dominated morphologies in the
denser group environment compared to the field, rather than to a reduced
propensity of the IHM in higher mass structures to cool and accrete onto
galaxies. We also suggest that the inferred substantial accretion of IHM gas by
satellite disk-dominated galaxies will lead to a progressive reduction in their
specific angular momentum, thereby representing an efficient secular mechanism
to transform morphology from star-forming disk-dominated types to more passive
spheroid-dominated types.
