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We generalize the classical Chevalley-Shephard-Todd theorem to the case offinite linearly reductive group schemes. As an application, we prove that everyscheme X which is etale locally the quotient of a smooth scheme by a finitelinearly reductive group scheme is the coarse space of a smooth tame Artinstack (as defined by Abramovich, Olsson, and Vistoli) whose stacky structure issupported on the singular locus of X.

The Chevalley–Shephard–Todd theorem for finite linearly reductive group schemes