  A conjectural generalization of the McKay correspondence in terms of stringy
invariants to arbitrary characteristic, including the wild case, was recently
formulated by the author in the case where the given finite group linearly acts
on an affine space. In cases of very special groups and representations, the
conjecture has been verified and related stringy invariants have been
explicitly computed. In this paper, we try to generalize the conjecture and
computations to more complicated situations such as non-linear actions on
possibly singular spaces and non-permutation representations of non-abelian
groups.
