  Let F be a local net of von Neumann algebras in four spacetime dimensions
satisfying certain natural structural assumptions. We prove that if F has
trivial superselection structure then every covariant, Haag-dual subsystem B is
the fixed point net under a compact group action on one component in a suitable
tensor product decomposition of F. Then we discuss some application of our
result, including free field models and certain theories with at most countably
many sectors.
