Flat Bundles with Solvable Holonomy

Let be a solvable linear Lie group. We show that for every flat principal -bundle over a CW-complex , there is a finite-sheeted covering space <!-- MATH $p:\hat M \to M$ --> such that <!-- MATH ${p^ * }\xi$ --> is trivial as a principal -bundle. This result is used to show that every affine manifold with solvable fundamental group has a finite covering which is parallelizable.