Flasque quasi-resolutions and non-surjectivity of the evaluation map for homogeneous spaces

The aim of this thesis is the study of R-equivalence classes of homogeneous spaces. For this purpose, the author introduces the concept of flasque quasi-resolution, which generalizes the better-known flasque resolutions introduced by Colliot-Thélène. The author employs them firstly to prove a stronger version of a theorem by Colliot-Thélène and Kunyavskii. Subsequently, the question arises whether the hypotheses of the proven theorem are necessary. Then, the author constructs two examples in which removing the hypotheses causes the claim to no longer hold, first on a field of cohomological dimension 2 and then on a 2-local field.