Microlocal analysis of Colombeau's generalized functions on a manifold

Various approaches to the space of Colombeau's generalized functions sigma(X) on a C-infinity-manifold X are analyzed. The wave front set of G epsilon sigma(X) is defined. The estimate of the wave front set for f*G, where f : X --> Y is a C-infinity-mapping and G epsilon sigma(Y), is given. The restriction on a submanifold is determined.