The paper presents a new semi-analytic model of galaxy formation that incorporates active galactic nuclei (AGN) feedback to explain the observed galaxy luminosity function and the evolution of galaxy stellar mass functions. The model is implemented within the Millennium N-body simulation and uses the ΛCDM cosmology. The key idea is that AGN feedback quenches cooling flows in massive haloes, leading to a break in the galaxy luminosity function at bright magnitudes. This mechanism naturally explains the observed 'antihierarchical' galaxy formation, where massive galaxies form earlier and have lower star formation rates than expected in a hierarchical model. The model predicts a substantial population of massive galaxies out to redshift z ∼ 5 and a star formation rate density that rises at least out to z ∼ 2. The model also explains the red colours of the most massive galaxies, which are not young and blue as expected in a hierarchical model. The model incorporates AGN feedback through a self-regulating feedback loop, where the energy injected by AGN is determined by the Eddington limit on the available power. The model is compared with observational data on the local and high-redshift Universe, showing good agreement with the observed galaxy luminosity function and stellar mass function. The model also predicts that massive galaxies were already in place at redshift z ∼ 4 with a stellar mass function similar to that observed. The model provides a good match to the observed star formation rate density and shows that the star formation history of the Universe is characterized by 'cosmic downsizing', where massive galaxies form earlier and have lower star formation rates than smaller galaxies. The model incorporates AGN feedback to explain the observed properties of the galaxy population and provides a robust framework for understanding galaxy formation in the ΛCDM cosmology.The paper presents a new semi-analytic model of galaxy formation that incorporates active galactic nuclei (AGN) feedback to explain the observed galaxy luminosity function and the evolution of galaxy stellar mass functions. The model is implemented within the Millennium N-body simulation and uses the ΛCDM cosmology. The key idea is that AGN feedback quenches cooling flows in massive haloes, leading to a break in the galaxy luminosity function at bright magnitudes. This mechanism naturally explains the observed 'antihierarchical' galaxy formation, where massive galaxies form earlier and have lower star formation rates than expected in a hierarchical model. The model predicts a substantial population of massive galaxies out to redshift z ∼ 5 and a star formation rate density that rises at least out to z ∼ 2. The model also explains the red colours of the most massive galaxies, which are not young and blue as expected in a hierarchical model. The model incorporates AGN feedback through a self-regulating feedback loop, where the energy injected by AGN is determined by the Eddington limit on the available power. The model is compared with observational data on the local and high-redshift Universe, showing good agreement with the observed galaxy luminosity function and stellar mass function. The model also predicts that massive galaxies were already in place at redshift z ∼ 4 with a stellar mass function similar to that observed. The model provides a good match to the observed star formation rate density and shows that the star formation history of the Universe is characterized by 'cosmic downsizing', where massive galaxies form earlier and have lower star formation rates than smaller galaxies. The model incorporates AGN feedback to explain the observed properties of the galaxy population and provides a robust framework for understanding galaxy formation in the ΛCDM cosmology.