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We develop the Schwinger-DeWitt technique for the covariant curvatureexpansion of the quantum effective action for brane induced gravity models incurved spacetime. This expansion has a part nonanalytic in DGP type scaleparameter, leading to the cutoff scale which is given by the geometric averageof the mass of the quantum field in the bulk and DGP scale. This cutoff is muchhigher than the analogous strong coupling scale of the DGP model treated byweak field expansion in the tree-level approximation. The lowest orders of thiscurvature expansion are calculated for the case of the scalar field in the$(d+1)$-dimensional bulk with the brane carrying the $d$-dimensional kineticterm of this field. The ultraviolet divergences in this model are obtained fora particular case of $d=4$.

The Schwinger-DeWitt technique for quantum effective action in brane induced gravity models