Feedback from the central black hole in active galactic nuclei (AGNs) may be responsible for establishing the observed MBH–σ relation and limiting the bulge stellar mass of the host galaxy. Here we explore the possibility of AGN feedback triggering star formation in the host galaxy. We consider a shell of dusty gas, driven outwards by radiation pressure, and analyse its escape/trapping condition in the galactic halo for different underlying dark matter potentials. In the isothermal potential, we obtain that the standard condition setting the observed MBH–σ relation is not sufficient to clear gas out of the entire galaxy, whereas the same condition is formally sufficient in the case of the Hernquist and Navarro–Frenk–White profiles. The squeezing and compression of the inhomogeneous interstellar medium during the ejection process can trigger star formation within the feedback-driven shell. We estimate the resulting star formation rate and total additional stellar mass. In this picture, new stars are formed at increasingly larger radii and successively populate the outer regions of the host galaxy. This characteristic pattern may be compared with the observed ‘inside-out’ growth of massive galaxies.