| We will discuss the R-group conjectured by Arthur. We address the question of which properties of the classical Knapp-Stein R-groups carry over to Arthur's setting, with somewhat surprising results. Some of the basic properties fail: the normalized standard intertwining operators in general do not form a basis of the commuting algebra and the components of the induced representation are not in a bijective correspondence with the irreducible representations of R. However, the action of standard intertwining operators on the induced space has a natural description in terms of representations of a finite group and the corresponding trace formulation holds. This is joint work with Chris Jantzen. |