The two-dimensional Hubbard model for interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the high-Tc cuprates. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom, bosonic fields are introduced which correspond to different collective orders, for example magnetism and superconductivity. The interactions between bosons and fermions are ...