  In a previous paper it was shown that a certain family of varieties suggested
by Lusztig, is not enough to construct all irreducible complex representations
of reductive groups over finite rings coming from the ring of integers in a
local field, modulo a power of the maximal ideal. In this paper we define a
generalisation of Lusztig's varieties, corresponding to an extension of the
maximal unramified extension of the local field. We show in a particular case
that all irreducible representations appear in the cohomology of some extended
variety. We conclude with a discussion about reformulation of Lusztig's
conjecture.
