Resumen de Affine Grassmannians in A1 -homotopy theory

Tom Bachmann

• Let k be a field. Denote by Spc(k)∗ the unstable, pointed motivic homotopy category and by RA1ΩGm:Spc(k)∗→Spc(k)∗ the ( A1 -derived) Gm -loops functor. For a k-group G, denote by GrG the affine Grassmannian of G. If G is isotropic reductive, we provide a canonical motivic equivalence RA1ΩGmG≃GrG . We use this to compute the motive M(RA1ΩGmG)∈DM(k,Z[1/e]) .