  We introduce the notion of Demazure descent data on a triangulated category C
and define the descent category for such data. We illustrate the definition by
our basic example. Let G be a reductive algebraic group with a Borel subgroup
B. Demazure functors form Demazure descent data on the derived category of
Rep(B) and the descent category is equivalent to the derived category of
Rep(G).

Representation Theory