Highest weight category structures on $Rep(B)$ and full exceptional collections on flag varieties over Z

This paper constructs full exceptional collections in the bounded derived categories of coherent sheaves of flag schemes of Chevalley group schemes over Z. The ensuing semiorthogonal decompositions are compatible with the Bruhat order on Weyl groups. The terms of full exceptional collections are a priori complexes of coherent sheaves; the question whether they are actually coherent sheaves is to be investigated further. The 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 $G/B$.