Hodge Cohomology of Étale Nori Finite Vector Bundles

Étale Nori finite vector bundles are the bundles defined by representations of a finite étale group scheme in the usual way. In this article, we show that in many cases the dimensions of the Hodge cohomology groups of such a vector bundle and a twist of it by an automorphism of the ground field are the same. This generalizes to the higher rank case the result of Pink–Roessler [13, Proposition 3.5].