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

L-group

In mathematics, L-group may refer to the following groups:* The Langlands dual, LG, of a reductive algebraic group G* A group in L-theory, L...

 is the connected component of the centralizer of a semisimple element of the L-group of G.

In the stable trace formula, unstable orbital integral

Orbital integral

In mathematics, an orbital integral is an integral transform that generalizes the spherical mean operator to homogeneous spaces. Instead of integrating over spheres, one integrates over generalized spheres: for a homogeneous space X = G/H, a generalized sphere centered at a point x0 is...

s on a group G correspond to stable orbital integrals on its endoscopic groups H.