Weighted Ehrhart theory and orbifold cohornology

We introduce the notion of a weighted delta-vector of a lattice polytope. Although the definition is motivated by motivic integration, we study weighted delta-vectors from a combinatorial perspective. We present a version of Ehrhart Reciprocity and prove a change of variables formula. We deduce a new geometric interpretation of the coefficients of the Ehrhart delta-vector. More specifically, they are sums of dimensions of orbifold cohomology groups of a toric stack. (c) 2008 Elsevier Inc. All rights reserved.