  We study a system of ultracold fermionic Potassium (40K) atoms in a
three-dimensional optical lattice in the vicinity of an s-wave Feshbach
resonance. Close to resonance, the system is described by a multi-band
Bose-Fermi Hubbard Hamiltonian. We derive an effective lowest-band Hamiltonian
in which the effect of the higher bands is incorporated by a self-consistent
mean-field approximation. The resulting model is solved by means of Generalized
Dynamical Mean-Field Theory. In addition to the BEC/BCS crossover we find a
phase transition to a fermionic Mott insulator at half filling, induced by the
repulsive fermionic background scattering length. We also calculate the
critical temperature of the BEC/BCS-state and find it to be minimal at
resonance.
