We generalize the modular Koszul duality of Achar-Riche to the setting of Soergel bimodules associated to any finite Coxeter system. The key new tools are a functorial monodromy action and wall-crossing functors in the mixed modular derived category. In characteristic 0, this duality together with Soergel's conjecture (proved by Elias-Williamson) imply that our Soergel-theoretic graded category @math is Koszul self-dual, generalizing the result of Beilinson-Ginzburg-Soergel.
For finite dihedral groups @math , the Koszulity and Koszul self-duality of @math was proved earlier by explicit methods by Sauerwein @cite_5 .
@cite_5
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We show that the endomorphism ring of the projective generator in the category of Soergel modules (for dihedral groups) is Koszul self-dual.