Classification of subsystems for local nets with trivial superselection structure

Let F be a local net of von Neumann algebras in four spacetime dimensions s atisfying certain natural structural assumptions. We prove that if F has tr ivial superselection structure then every covariant, Haag-dual subsystem B is of the form F-1(G) x I for a suitable decomposition F = F-1 x F-2 and a compact group action. Then we discuss some application of our result, inclu ding free field models and certain theories with at most countably many sec tors.