Combinatorics of characters of Hecke algebras and Chevalley groups

The object of interest is the trace of the action of GL(F_q) and the Iwahori-Hecke algebra on flags. There are several different formulas and interpretations of the trace: in terms of (1) column strict tableaux, (2) weighted words, (3) Green polynomials, (3) Hall-Littlewood symmetric functions (4) Kostka-Foulkes polynomials and (5) the number of F-rational points of a certain variety. I shall summarize these interpretations and discuss the information that this trace provides about the characters of Iwahori-Hecke algebras.