Relative Kazhdan-Lusztig isomorphism

The Kazhdan–Lusztig isomorphism, relating the affine Hecke algebra of a p-adic group to the equivariant K-theory of the Steinberg variety of its Langlands dual, played a key role in the proof of the Deligne–Langlands conjectures concerning the classification of tamely ramified irreducible representations. In this talk, I will recall the statement of the Kazhdan–Lusztig isomorphism. I will also introduce the relative Langlands duality and propose a conjectural relative version of the Kazhdan–Lusztig isomorphism. I will focus on specific examples which we can prove.