We consider some function field analogs of some main cohomological results of Kottwitz theory used in stable trace formula and Colliot-Thélène (and Sansuc) theory and give some applications.
"On Galois cohomology and weak approximation of connected reductive groups over fields of positive characteristic." Proc. Japan Acad. Ser. A Math. Sci. 87 (10) 203 - 208, December 2011. https://doi.org/10.3792/pjaa.87.203