  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.
