  We classify principal bundles over anti-affine schemes with affine and
commutative structural group. We show that this yields the classification of
quasi-abelian varieties over a field k (i.e., group k-schemes with no non
constant global functions). The interest of this result is given by the fact
that the classification of smooth group k-schemes is reduced to the
classification of quasi-abelian varieties and of certain affine group schemes.
