  We consider a resonantly-interacting Bose-Fermi mixture of $^{40}$K and
$^{87}$Rb atoms in an optical lattice. We show that by using a red-detuned
optical lattice the mixture can be accurately described by a generalized
Hubbard model for $^{40}$K and $^{87}$Rb atoms, and $^{40}$K-$^{87}$Rb
molecules. The microscopic parameters of this model are fully determined by the
details of the optical lattice and the interspecies Feshbach resonance in the
absence of the lattice. We predict a quantum phase transition to occur in this
system already at low atomic filling fraction, and present the phase diagram as
a function of the temperature and the applied magnetic field.
