CAP-Localization

Abstract

In this chapter, we will express the π-isotypic Lefschetz numbers of Hecke operators acting on the cohomology of symmetric spaces SK(G) attached to reductive groups G in terms of so-called elliptic traces Tell, provided the underlying representation π is not a cuspidal representation associated with a parabolic subgroup (CAP representation) of G(A). In the following two chapters we derive from these formulas all the essential information required.