  The purpose of this paper is to use conservative descent to study
semi-orthogonal decompositions for some homogeneous varieties over general
bases. We produce a semi-orthogonal decomposition for the bounded derived
category of coherent sheaves on a generalized Severi-Brauer scheme. This
extends known results for Sever-Brauer varieties and Grassmanianns. We use our
results to construct semi-orthogonal decompositions for flag varieties over
arbitrary bases. This generalises a result of Kapranov.
