Abstract: This is a report on a joint work with Wilberd van der Kallen based on arxiv.org/abs/2407.13653. Given a split simply connected reductive group scheme G over a field k and a parabolic subscheme P of G, we construct G-linear semiorthogonal decompositions of the bounded derived category of rational P-modules, which are finitely generated over k. Each piece of such a semiorthogonal decomposition is equivalent, as a triangulated category, to the bounded derived category of rational G-modules, which are finitely generated over k, while the number of semiorthogonal components is equal to the cardinality of the Weyl group. The ensuing semiorthogonal decompositions are compatible with the Bruhat order on Weyl groups. Our construction builds upon the foundational results on B-modules from the works of Mathieu, Polo, and van der Kallen, and upon properties of the Steinberg basis of the T-equivariant K-theory of flag varieties G/B. As a corollary, one obtains full exceptional collections in the bounded derived categories of coherent sheaves on generalized flag schemes G/P of Chevalley group schemes over the integers. Time permitting, we will talk about a work in progress in which we relate our constructions in coherent categories to highest weight categories in the constructible setting and to perverse t-structures.