COSMOS-Web: From early star-formation enhancement to late suppression in galaxy groups

Galaxy groups trace dense environments where interactions, gas removal, and reduced accretion may drive quenching. Common diagnostics trace star formation over short timescales (100 Myr); time-resolved star formation histories (SFHs) separate recent changes from longer-term evolution at fixed mass and redshift. Using COSMOS-Web data, we test how group environment correlates with star-formation activity and its evolution with cosmic time and group-centric distance, contrasting high-richness groups with excluded field galaxies. We combine COSMOS2025/COSMOS-Web stellar masses and non-parametric SFHs with group detections and memberships from AMICO (Adaptive Matched Identifier of Clustered Objects), comparing stacked SFHs of matched group and field galaxies and measuring how the SFH offset evolves with group-centric distance for the richest groups. Massive galaxies ((M/M)>10.5) show the largest offsets but are already quenched in both environments. For lower masses (8.1< (M/M)<10.5), suppression is clearest at z<1.5 (deficit up to 0.8 dex), while at z>1.5 SFHs show weak suppression or occasional enhancement. The radial signal evolves similarly: quenching is broad at low z, the inner-outer contrast sharpens at z 1, and any ordering at z 2 is tentative given growing uncertainties in the AMICO centroids. These results suggest an evolving picture: groups are more mixed at early epochs, with both suppressed and occasionally elevated SFHs, partly reflecting high- z uncertainties, while suppression dominates from z 1.5, most clearly for low-to-intermediate-mass galaxies. Inner-region galaxies likely spend more time in the group potential, undergo more passages through dense intra-group gas, and accrete less pristine cold gas, making quenching progressively clearer with cosmic time.