  We develop the motivic integration theory over formal Deligne-Mumford stacks
over a power series ring of arbitrary characteristic. This is a generalization
of the corresponding theory for tame and smooth Deligne-Mumford 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. In fact, we prove a more general result, the invariance of
stringy motives of (stacky) log pairs under crepant morphisms.
