  Let $G$ be a reductive $p$--adic group. Assume that $L\subset G$ is an
open--compact subgroup, and $\mathcal H_L$ is the Hecke algebra of
$L$--biinivariant complex functions on $G$. It is a well--known and standard
result on how to prove existence of a complex smooth irreducible $G$--module
out of a maximal left ideal $I\subset \mathcal H_L$. Using theory on Bernstein
center we make this construction explicit. This leads us to some very
interesting questions.
