A motivic change of variables formula for Artin stacks

Let $\mathcal{X} \to Y$ be a birational map from a smooth Artin stack to a (possibly singular) variety. We prove a change of variables formula that relates motivic integrals over arcs of $Y$ to motivic integrals over arcs of $\mathcal{X}$. With a view toward the study of stringy Hodge numbers, this change of variables formula leads to a new notion of crepantness for the map $\mathcal{X} \to Y$ that coincides with the usual notion in the special case that $\mathcal{X}$ is a scheme.