### Abstract

Let G be a split semisimple linear algebraic group over a field k_{0}. Let E be a G-torsor over a field extension k of k_{0}. Let h be an algebraic oriented cohomology theory in the sense of Levine–Morel. Consider a twisted form E/B of the variety of Borel subgroups G/B over k. Following the Kostant–Kumar results on equivariant cohomology of flag varieties we establish an isomorphism between the Grothendieck groups of the h-motivic subcategory generated by E/B and the category of finitely generated projective modules of certain Hecke-type algebra H which depends on the root datum of G, on the torsor E and on the formal group law of the theory h. In particular, taking h to be the Chow groups with finite coefficients F_{p} and E to be a generic G-torsor we prove that all finitely generated projective indecomposable submodules of an affine nil-Hecke algebra H of G with coefficients in F_{p} are isomorphic to each other and correspond to the (non-graded) generalized Rost–Voevodsky motive for (G,p).

Original language | English |
---|---|

Pages (from-to) | 791-818 |

Number of pages | 28 |

Journal | Advances in Mathematics |

Volume | 340 |

DOIs | |

Publication status | Published - 15 Dec 2018 |

### Scopus subject areas

- Mathematics(all)

## Fingerprint Dive into the research topics of 'Motivic decompositions of twisted flag varieties and representations of Hecke-type algebras'. Together they form a unique fingerprint.

## Cite this

*Advances in Mathematics*,

*340*, 791-818. https://doi.org/10.1016/j.aim.2018.10.014