  In [Lu6] Lusztig defined a certain algebra $H,$ which is a direct sum of
various algebras $H_{\mathfrak{o}}.$ We establish an explicit algebra
isomorphism between each algebra $H_{\mathfrak{o}}$ and some matrix algebra
with coefficients in the tensor product of an (affine or finite) Hecke algebra
and a group algebra. We give an application.
