Motivic integration over wild Deligne-Mumford stacks
We develop the motivic integration theory over formal DeligneMumford stacks over a power series ring of arbitrary characteristic. This is a generalization of the corresponding theory for tame and smooth DeligneMumford stacks constructed in earlier papers of the author. As an application, we obtain the wild motivic McKay correspondence for linear actions of arbitrary finite groups, which has been known only for cyclic groups of prime order. In particular, this implies the motivic version of Bhargava’s mass formula as a special case, which was earlier proved in a joint work of Tonini and the author by a different method. In fact, we prove a more general result, the invariance of stringy motives of (stacky) log pairs under crepant morphisms.