  We consider atomic Bose-Fermi mixtures in optical lattices and study the
superfluidity of fermionic atoms due to s-wave pairing induced by boson-fermion
interactions. We prove that the induced fermion-fermion coupling is always {\it
attractive} if the boson-boson on site interaction is repulsive, and predict
the existence of an enhanced BEC--BCS crossover as the strength of the lattice
potential is varied. We show that for direct on-site fermion-fermion {\it
repulsion}, the induced attraction can give rise to superfluidity via s-wave
pairing, at striking variance with the case of pure systems of fermionic atoms
with direct repulsive interactions.
