The unramified Brauer group of quotients by algebraic groups

The report is based on Colliot-Thelene's and Sansuc's papers. Two theorems will be proved. The ground field is the field of complex numbers. 1. Let $G$ be a connected algebraic group and let $V$ be an almost free linear representation of $G$. Then the unramified Brauer group of the field of rational functions on $V/G$ is trivial. 2. Let $G$ be a connected simply connected algebraic group and let $H$ be its connected closed subgroup. Then the unramified Brauer group of $G/H$ is trivial.