Discrete series characters and the Lefschetz formula for Hecke operators
  This paper gives combinatorial formulas for discrete series constants, both stable and unstable, on real reductive groups. It also carries out one step of the comparison of the topological trace formula for Hecke operators with Arthur's trace formula for Hecke operators, the step in which the topological terms are combined in such a way that stable discrete series characters appear. 
Mark Goresky, Robert Kottwitz, and Robert MacPherson