A large body of observations shows that the galaxy properties change systematically with environment. According to the most popular scenario of galaxy formation,galaxies are born inside Cold Dark Matter (CDM) halos. Do the CDM haloassembly process and the properties of the halos depend on environment? Can these possible dependencies be at the basis of the observable galaxyproperties-environment correlations? By using high-resolution N-body cosmological simulations, we will provide some answers to these questions.