Crepant resolutions of quotients by finite linearly reductive group schemes in any characteristic have Euler number equal to the number of irreducible representations of the group.
A geometric invariant of a finite group
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abstract
We study the class of the classifying stack of a finite group in a Grothendieck group of algebraic stacks introduced previously. We show that this class is trivial in a number of examples most notably for all symmetric groups. We also give some examples where it is not trivial. The latter uses counterexamples of Saltman and Swan to the problem of Noether.
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McKay correspondence for linearly reductive finite group schemes in positive characteristic
Crepant resolutions of quotients by finite linearly reductive group schemes in any characteristic have Euler number equal to the number of irreducible representations of the group.