On the existence of a unipotent support for the irreducible characters of a finite group of Lie type

In 1980, Lusztig posed the problem of showing the existence of a unipotent support for the irreducible characters of a finite group of Lie type. This problem was solved by Lusztig in the case where the characteristic of the f ield over which the group is defined is large enough. The first named autho r extended this to the case where the characteristic is good. It is the pur pose of this paper to remove this condition as well, so that the existence of unipotent supports is established in complete generality.