Stable trace formula: Cuspidal tempered terms (Q1065172)

Let G be a reductive group over a number field F. The meaning and the importance of a ''stable'' trace formula for G are explained by \textit{R. P. Langlands} in ''Les débuts d'une formule des traces stable'' [Publ. Math. Univ. Paris VII, 13 (1983; Zbl 0532.22017)]. There he gives explicitly the stabilization of the regular elliptic part of the trace formula. In particular, he defines, for any elliptic endoscopic group H of G, a number \(\iota\) (G,H) relating the stable trace formula for H to the trace formula for G. In the present paper the author proves an identity for \(\iota\) (G,H) involving Tamagawa numbers. He uses this expression for \(\iota\) (G,H) in a ''speculative'' consideration concerning the tempered cuspidal part of the trace formula and its stabilization.