2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98338We construct a certain topological algebra $\Ext ^{\sharp}_{G ^{\vee}} X (χ)$ from a Deligne-Langlands parameter space $X (χ)$ attached to the group of rational points of a connected split reductive algebraic group $G$ over a non-Archimedean local field $\mathbb K$. Then we prove the equivalence between the category of continuous modules of $\Ext ^{\sharp}_{G ^{\vee}} X (χ)$ and the category of unramified admissible modules of $G (\mathbb K)$ with a generalized infinitesimal character corresponding to $χ$. This is an analogue of Soergel's conjecture which concerns the real reductive setting.v2. added a section about equivariant derived category and fixed a name about Soergel's question, 15pp, to appear in Publ. RIMSRepresentation TheoryRings and Algebrastext