  Let X be a homogeneous space of a quasi-trivial k-group G, with geometric
stabilizer H, over a number field k. We prove that under certain conditions on
the character group of H, certain algebraic Brauer-Manin obstructions to the
Hasse principle and weak approximation vanish, because the abelian groups where
they take values vanish. When H is connected or abelian, these algebraic
Brauer-Manin obstructions to the Hasse principle and weak approximation are the
only ones, so we prove the Hasse principle and weak approximation for X under
certain conditions. As an application, we obtain new sufficient conditions for
the Hasse principle and weak approximation for linear algebraic groups.
