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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 ofEhrhart Reciprocity and prove a change of variables formula. We deduce a newgeometric interpretation of the coefficients of the Ehrhart $\delta$-vector.More specifically, they are sums of dimensions of orbifold cohomology groups ofa toric stack.

Weighted Ehrhart Theory and Orbifold Cohomology