The motivic Satake equivalence

We refine the geometric Satake equivalence due to Ginzburg, Beilinson-Drinfeld, and Mirković-Vilonen to an equivalence between mixed Tate motives on the double quotient $L^+G∖LG/L^+G$ and representations of Deligne's modification of the Langlands dual group of G. This yields a formulation of the Satake equivalence which is independent of the choice of cohomology theory (in particular, independent of $\ell$ in an arithmetic context). This is joint work with Timo Richarz.