  Let w be an element of the Weyl group of a reductive group G defined and
split over a finite field. We consider the variety of triples (g,B,B') where g
is a unipotent element of G and B, B' are Borel subgroups of G such that B
contains g and B',gB'g^{-1} are in relative position w. We show that the number
of rational points of this variety can be expressed in terms of a trace on the
Iwahori-Hecke algebra. We also show that this variety is smooth, irreducible,
if w is elliptic, of minimal length in its conjugacy class.
