We present the data release of the Gemini-South GMOS spectroscopy in the fields of 11 galaxy groups at 0.8<z<1, within the COSMOS field. This forms the basis of the Galaxy Environment Evolution Collaboration 2 (GEEC2) project to study galaxy evolution in haloes with M~10^13^M_{sun}_ across cosmic time. The final sample includes 162 spectroscopically confirmed members with R<24.75, and is >50% complete for galaxies within the virial radius, and with stellar mass M_star_>10^10.3^M_{sun}_. Including galaxies with photometric redshifts, we have an effective sample size of ~400 galaxies within the virial radii of these groups. We present group velocity dispersions, dynamical and stellar masses. Combining with the GCLASS sample of more massive clusters at the same redshift, we find the total stellar mass is strongly correlated with the dynamical mass, with logM_200_=1.20(logM_star_-12)+14.07. This stellar fraction of ~1% is lower than predicted by some halo occupation distribution models, though the weak dependence on halo mass is in good agreement. Most groups have an easily identifiable most massive galaxy (MMG) near the centre of the galaxy distribution, and we present the spectroscopic properties and surface brightness fits to these galaxies. The total stellar mass distribution in the groups, excluding the MMG, compares well with an NFW (Navarro Frenk & White) profile with concentration 4, for galaxies beyond ~0.2R_200_. This is more concentrated than the number density distribution, demonstrating that there is some mass segregation.