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The observed massive end of the galaxy stellar mass function is steeper thanits predicted dark matter halo counterpart in the standard $\Lambda $CDMparadigm. In this paper, we investigate the impact of active galactic nuclei(AGN) feedback on star formation in massive galaxies. We isolate the impact ofAGNs by comparing two simulations from the HORIZON suite, which are identicalexcept that one also includes super massive black holes (SMBH), and relatedfeedback models. This allows us to cross-identify individual galaxies betweensimulations and quantify the effect of AGN feedback on their properties,including stellar mass and gas outflows. We find that massive galaxies ($ \rmM_{*} \geq 10^{11} M_\odot $) are quenched by AGN feedback to the extent thattheir stellar masses decrease by up to 80% at $z=0$. SMBHs affect their hosthalo through a combination of outflows that reduce their baryonic mass,particularly for galaxies in the mass range $ \rm 10^9 M_\odot \leq M_{*} \leq10^{11} M_\odot $, and a disruption of central gas inflows, which limitsin-situ star formation. As a result, net gas inflows onto massive galaxies, $\rm M_{*} \geq 10^{11} M_\odot $, drop by up to 70%. We measure a redshiftevolution in the stellar mass ratio of twin galaxies with and without AGNfeedback, with galaxies of a given stellar mass showing stronger signs ofquenching earlier on. This evolution is driven by a progressive flattening ofthe $\rm M_{\rm SMBH}-M_* $ relation with redshift, particularly for galaxieswith $\rm M_{*} \leq 10^{10} M_\odot $. $\rm M_{\rm SMBH}/M_*$ ratios decreaseover time, as falling average gas densities in galaxies curb SMBH growth.

Cosmic evolution of stellar quenching by AGN feedback: clues from the Horizon-AGN simulation