We study the evolution of the total star formation (SF) activity, total stellar mass (∑M*) and halo occupation distribution (HOD) in massive haloes by using one of the largest X-ray selected sample of galaxy groups with secure spectroscopic identification in the major blank field surveys (ECDFS, CDFN, COSMOS, AEGIS). We provide an accurate measurement of star formation rate (SFR) for the bulk of the star-forming galaxies using very deep mid-infrared Spitzer MIPS and far-infrared Herschel PACS observations. For undetected IR sources, we provide a well-calibrated SFR from spectral energy distribution (SED) fitting. We observe a clear evolution in the level of SF activity in galaxy groups. The total SF activity in the high-redshift groups (0.5 < z < 1.1) is higher with respect to the low-redshift (0.15 < z < 0.5) sample at any mass by 0.8 ± 0.12 dex. A milder difference (0.35 ± 0.1 dex) is observed between the low-redshift bin and the groups at z ~ 0. We show that the level of SF activity is declining more rapidly in the more massive haloes than in the more common lower mass haloes. We do not observe any evolution in the HOD and total stellar mass-halo mass relations in groups. The picture emerging from our findings suggests that the galaxy population in the most massive systems is evolving faster than galaxies in lower mass haloes, consistently with a 'halo downsizing' scenario.

Using data from four deep fields (COSMOS, AEGIS, ECDFS, and CDFN), we study the correlation between the position of galaxies in the star formation rate (SFR) versus stellar mass plane and local environment at $z<1.1$. To accurately estimate the galaxy SFR, we use the deepest available Spitzer/MIPS 24 and Herschel/PACS datasets. We distinguish group environments ( $M_{halo}\sim$10$^{12.5-14.2}$$M_{\odot}$) based on the available deep X-ray data and lower halo mass environments based on the local galaxy density. We confirm that the Main Sequence (MS) of star forming galaxies is not a linear relation and there is a flattening towards higher stellar masses ( $M_*>10^{10.4-10.6}$ $M_{\odot}$), across all environments. At high redshift ( $0.5