Does an active supermassive black hole affect the properties of the galaxy it lives in?

In the last decade there has been growing evidence supporting the coeval growth of galaxies and their resident Supermassive Black Hole (SMBH). However, it is still not clear what are the physical mechanisms that drive the black hole (BH) growth, how the large-scale environment (the mass of their Dark Matter Halo, DMHM) affects these feeding mechanisms and what is the connection between the environment of the SMBH and the host galaxy properties, e.g. Star- Formation Rate (SFR) and stellar mass (M⋆).