Duals of orbit spaces in groups with relatively compact inner automorphism groups are hypergroups

For a locally compact group G and a group B of topological automorphisms containing the inner automorphisms of G and being relatively compact with respect to Birkhoff topology (that is G∈[FIA]_B, B {Mathematical expression}I(G)) the space G_B of {Mathematical expression}-orbits is a commutative hypergroup (=commutative convo in Jewett's terminology) in a natural way as Jewett has shown. Identifying the space of hypergroup characters of G_B with E(G, B) (the extreme points of B-invariant positive definite continuous functions p with p (e)=1, endowed with the topology of compact convergence) we prove that E(G, B) is a hypergroup, the "hypergroup dual" of G_B.