Scientific group
In mathematics, endoscopic groups of reductive algebraic groups were introduced by Robert Langlands (1979, 1983) 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.