  Applying the authors' preceding work, we construct a version of the moduli
space of $G$-torsors over the formal punctured disk for a finite group $G$. To
do so, we introduce two Grothendieck topologies, the sur (surjective) and luin
(locally universally injective) topologies, and define P-schemes using them as
variants of schemes. Our moduli space is defined as a P-scheme approximating
the relevant moduli functor. We then prove that Fr\"ohlich's module resolvent
gives a locally constructible function on this moduli space, which implies that
motivic integrals appearing the wild McKay correspondence are well-defined.
