DMS-9500880 PI: Shelstad Shelstad will investigate the twisted endoscopy of connected reductive algebraic groups over local fields. It is planned to develop descent theory for transfer factors and applying it to some pivotal questions in transfer of twisted orbital integrals. An overall goal is to establish results applicable to stabilization of the adelic twisted trace formula and the study of automorphic representations, especially multiplicity formulas. The theory of Lie groups, named in honor of the Norwegian mathematician Sophus Lie, has been one of the major themes in twentieth century mathematics. As the mathematical vehicle for exploiting the symmetries inherent in a system, the representation theory of Lie groups has had a profound impact upon mathematics itself, particularly in analysis and number theory, and upon theoretical physics, especially quantum mechanics and elementary particle physics.