  We show that feedback from active galactic nuclei (AGN) plays an essential
role in reproducing the down-sizing phenomena, namely: the colour-magnitude
relation; specific star formation rates; and the $\alpha$ enhancement of early
type galaxies. In our AGN model, black holes originate from Population III
stars, in contrast to the merging scenario of previous works. In this paper, we
show how the properties of present-day galaxies in cosmological
chemo-hydrodynamical simulations change when we include our model for AGN
feedback. Massive galaxies become redder, older, less massive, less compact,
and show greater $\alpha$ enhancement than their counterparts without AGN.
Since we reproduce the black hole mass and galaxy mass relation, smaller
galaxies do not host a supermassive black hole and their star formation history
is affected very little, but they can get external enrichment from nearby AGN
depending on their environment. Nonetheless, the metallicity change is
negligible, and the mass--metallicity relations, which are mainly generated by
supernova feedback at the first star burst, are preserved.
