Let M = R_s~n /Γ be a complete flat pseudo-Riemannian homogeneous manifold, Γ ? Iso(R_s~n) its fundamental group and G the Zariski closure of Γ in Iso(R_s~n). We show that the G-orbits in R_s~n are affine subspaces and affinely diffeomorphic to G endowed with the (0)-connection. If the restriction of the pseudo-scalar product on R_s~n to the G-orbits is nondegenerate, then M has abelian linear holonomy. If additionally G is not abelian, then G contains a certain subgroup of dimension 6. In particular, for non-abelian G, orbits with non-degenerate metric can appear only if dimG ≥ 6. Moreover, we show that R_s~n is a trivial algebraic principal bundle G → M → R~(n?k). As a consquence, M is a trivial smooth bundle G/Γ → M → R~(n?k) with compact fiber G/Γ.
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