  We give a simplified proof (in characteristic zero) of the decomposition
theorem for complex projective varieties with klt singularities and numerically
trivial canonical bundle. The proof rests in an essential way on most of the
partial results of the previous proof obtained by many authors, but avoids
those in positive characteristic by S. Druel. The single to some extent new
contribution is an algebraicity and bimeromorphic splitting result for
generically locally trivial fibrations with fibres without holomorphic vector
fields. We give first the proof in the easier smooth case, following the same
steps as in the general case, treated next.
