| Résume | In this talk, we construct a geometric realisation of the category of representations of the affine Hecke algebra.
For this, we introduce a formalism of K-theoretic sheaves (called K-motives) on stacks.
The affine Hecke algebra arises from the K-theory of the Steinberg stack, and we explain how to “categorify” this using K-motives.
Lastly, we briefly discuss the relation to the local geometric Langlands and the coherent Springer theory of Ben-Zvi, Chen, Helm, and Nadler. |
