Open problems in the wild McKay correspondence and related fields

The wild McKay correspondence is a form of McKay correspondence in terms of stringy invariants that is generalized to arbitrary characteristics. It gives rise to an interesting connection between the geometry of wild quotient varieties and arithmetic on extensions of local fields. The principal purpose of this article is to collect open problems on the wild McKay correspondence, as well as those in related fields that the author believes are interesting or important. It also serves as a survey on the present state of these fields.