  We show that the Cappell-Shaneson version of Pick's theorem for simple
lattice polytopes is a consequence of a general relation between characteristic
numbers of virtual submanifolds dual to the characteristic classes of a stably
almost complex manifold. This relation is analogous to the miraculous
cancellation formula of Alvarez-Gaume and Witten, and is imposed by the action
of the Landweber-Novikov algebra in the complex cobordism ring of a point.
