Let G be a split semisimple linear algebraic group over a field k, let Ebe a G-torsor over k. Let h be an algebraic oriented cohomology theory inthe sense of Levine-Morel (e.g.~Chow ring or an algebraic cobordism).Consider a twisted form E/B of the variety of Borel subgroups G/B.Following Brion’s and Kostant-Kumar’s results on equivariant cohomology offlag varieties we establish an equivalencebetween the h-motivic subcategory generated by E/B and the category ofprojective modules of certain Hecke-type algebra H which depends on theroot system of G, its isogeny class, on E, and on the formal group law ofthe theory h. In particular, taking h to be the Chow groups with finite coefficients F_pand E to be a generic torsor we obtain that all irreducible submodules oftheaffine nil-Hecke algebra H of G with coefficients in F_p are isomorphicand correspond to the generalized Rost-Voevodsky motive for (G,p).
- Variétés rationnelles