  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 $\mathcal{O}$ is Koszul self-dual,
generalizing the result of Beilinson-Ginzburg-Soergel.
