  Understanding the mechanisms that lead dense environments to host galaxies
with redder colors, more spheroidal morphologies, and lower star formation
rates than field populations remains an important problem. As most candidate
processes ultimately depend on host halo mass, accurate characterizations of
the local environment, ideally tied to halo mass estimates and spanning a range
in halo mass and redshift are needed. In this work, we present and test a
rigorous, probabalistic method for assigning galaxies to groups based on
precise photometric redshifts and X-ray selected groups drawn from the COSMOS
field. The groups have masses in the range 10^13 < M_200c/M_sun < 10^14 and
span redshifts 0<z<1. We characterize our selection algorithm via tests on
spectroscopic subsamples, including new data obtained at the VLT, and by
applying our method to detailed mock catalogs. We find that our group member
galaxy sample has a purity of 84% and completeness of 92% within 0.5 R200c. We
measure the impact of uncertainties in redshifts and group centering on the
quality of the member selection with simulations based on current data as well
as future imaging and spectroscopic surveys. As a first application of our new
group member catalog which will be made publicly available, we show that member
galaxies exhibit a higher quenched fraction compared to the field at fixed
stellar mass out to z~1, indicating a significant relationship between star
formation and environment at group scales. We also address the suggestion that
dusty star forming galaxies in such groups may impact the high-l power spectrum
of the cosmic microwave background and find that such a population cannot
explain the low power seen in recent SZ measurements.
