Orbits of a symmetric subgroup in the Bruhat-Tits building

Overview & Synopsis

Let G be a connected reductive algebraic group defined over a nonarchimedean locally compact field F of odd residue characteristic. Let θ be an F -rational involution of G and H be the reductive F -group G θ . We describe the orbits of the symmetric subgroup H F in the set of chambers of the reduced building of G over F.