I was reading this paper by Baues and on page 918 he mention that $S$ acts reductively on the cochain complex and on page 919 again he mention the word "Since $T$ acts reductively on the complex...". I have tried searching for the meaning of this everywhere but I could not find the usage of this word. Maybe because I am not an expert in linear algebraic group theory I dont know where to find it. Please help me I really need to know the meaning of this.
Moreover, if a linear algebraic group acts reductively on a cochain complex why does it acts trivially on the cohomology of that cochain complex?