Endoscopic group

In mathematics, endoscopic groups of reductive algebraic groups were introduced by in his work on the stable trace formula.
Roughly speaking, an endoscopic group "H" of "G" is a quasi-split group whose L-group is the connected component of the centralizer of a semisimple element of the L-group of "G".
In the stable trace formula, unstable orbital integrals on a group "G" correspond to stable orbital integrals on its endoscopic groups "H". The relation between them is given by the fundamental lemma.