Finite groups as algebraic groups in defining characteristic

We will discuss p-local representation theory and conjectures of Broue and Alperin, the latter been inspired by finite groups of Lie type in characteristic p. The issue is the extent to which the category of representations can be reconstructed from that of proper parabolic subgroups. In different settings, a Borel suffices (Arkhipov-Bezrukavnikov-Ginzburg for rational representations, Colmez for GL2 over ℚp).