Kazhdan and Lusztig proved the Deligne-Langlands conjecture, a bijection between irreducible representations of principal block representations of a p-adic group with certain unipotent Langlands parameters (a q-commuting semisimple-nilpotent pair) in the Langlands dual group. We lift this bijection to a statement on the level of categories. Namely, we define a stack of unipotent Langlands parameters and a coherent sheaf on it, which we call the coherent Springer sheaf, which generates a subcategory of the derived category of coherent sheaves equivalent to modules for the affine Hecke algebra (or specializing at q, smooth principal block representations of a p-adic group). Our approach involves categorical traces, Hochschild homology, and Bezrukavnikov’s Langlands dual realizations of the affine Hecke category. This is a joint work with David Ben-Zvi, David Helm and David Nadler.