  Using the results of J. Arthur on the representation theory of classical
groups with additional work by Colette Moeglin and its relation with
representations of affine Hecke algebras established by the author, we show
that the category of smooth complex representations of a split $p$-adic
classical group and its pure inner forms is naturally decomposed into
subcategories which are equivalent to a tensor product of categories of
unipotent representations of classical groups (in the sense of G. Lusztig). A
statement of this kind had been conjecture by G. Lusztig. All classical groups
(general linear, orthogonal, symplectic and unitary groups) appear in this
context. We get also parameterizations of representations of affine Hecke
algebras, which seem not all to be in the literature yet. All this should also
shed some light on what is known as the stable Bernstein center.
