Ergodic actions of compact matrix pseudogroups on C*-algebras

A generalization of the classical finiteness theorem of Hoegh-Krohn, Landstad and Stormer for ergodic actions of compact groups on operator algebras is proved for actions of compact matrix pseudogroups on C*-algebras. This, together with the Takesaki-Takai type duality result of Baaj and Skandalis, show that the reduced C*-crossed product of a unital C*-algebra by an ergodic action of a compact matrix pseudogroup is a direct sum of C*-algebras of compact operators.