Abstract

We give formulas for calculating the unramified Brauer group of a homogeneous space X of a semisimple simply connected group G with finite geometric stabilizer (F) over bar over a wide family of fields of characteristic 0. When k is a number field, we use these formulas in order to study the Brauer-Manin obstruction to the Hasse principle and weak approximation. We prove in particular that the Brauer-Manin pairing is constant on X(k(v)) for every v outside of an explicit finite set of nonarchimedean places of k.