Koszul duality for Kac–Moody groups and characters of tilting modules

We establish a character formula for indecomposable tilting modules for connected reductive groups in characteristicℓ terms ofℓ-Kazhdan–Lusztig polynomials, forℓ>h > hthe Coxeter number. Using results of Andersen, one may deduce a character formula for simple modules ifℓ≥2h−2 ≥ 2h-2. Our results are a consequence of an extension to modular coefficients of a monoidal Koszul duality equivalence established by Bezrukavnikov and Yun.