  We present the theory for ultracold atomic gases in an optical lattice near a
Feshbach resonance. In the single-band approximation the theory describes atoms
and molecules which can both tunnel through the lattice. Moreover, an avoided
crossing between the two-atom and the molecular states occurs at every site. We
determine the microscopic parameters of the generalized Hubbard model that
describes this physics, using the experimentally known parameters of the
Feshbach resonance in the absence of the optical lattice. As an application we
also calculate the zero-temperature phase diagram of an atomic Bose gas in an
optical lattice.
