  We construct a certain topological algebra $\Ext ^{\sharp}_{G ^{\vee}} X
(\chi)$ from a Deligne-Langlands parameter space $X (\chi)$ 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 $\Ext ^{\sharp}_{G ^{\vee}} X
(\chi)$ and the category of unramified admissible modules of $G (\mathbb K)$
with a generalized infinitesimal character corresponding to $\chi$. This is an
analogue of Soergel's conjecture which concerns the real reductive setting.
