Twisted orbital integrals on real reductive Lie groups (Q1355075)

The author studies the orbital integrals on non-connected real reductive groups, obtaining a characterisation of these functions. In this context he constructs a family of invariant eigendistributions that are used to prove an invariant Paley-Wiener theorem. The article consists of 18 sections, among them the most important ones are: Section 9 -- Orbital integrals, Section 15 -- Construction of proper invariant distributions, and Section 17 -- Invariant Paley-Wiener theorem.