Diagrams encoding group actions on $\Gamma$-spaces
  We introduce, for any group $G$, a category $G\Gamma$ such that diagrams $G\Gamma \rightarrow \mathcal{SS}ets$ satisfying a Segal condition correspond to infinite loop spaces with a $G$-action. We also consider diagrams which encode group actions on infinite loop spaces where the group may vary. 
Julia E. Bergner and Philip Hackney
math.AT