On p. 60 ff. of Steenrods "Cohomology Operations" which can be downloaded freely (just google, first result), the group action of a group $G $ on a cell complex $K $ is mentioned. For me a cell complex is nothing but a CW complex. Otherwise he uses on p. 58 the $K $ as a chain complex on which $G $ acts from the left. So I am a little bit confused what he actually means. Therefore:
1.) What is a group action on a cell complex $K $ with respect to the cell structure? How can I imagine it (graphically)?
2.) The same questions for group actions on chain complexes.
Then he mentions "a $G $-subcomplex of a $G $-free cell complex" (p. 60) and $G $-basis for cells.
3.) Does $G$-free cell complex mean "free" in the sense of modules? But in which sense is this cell complex a module? (Left $G $-module?)
4.) What is meant by $G $-subcomplex and $G $-basis for cells?
I think the questions shouldn't be hard, but indicate my lack of knowledge with respect to $G$-actions in the context of algebraic topology. I would be thankful for easy understandable answers with some examples.
Edit: I think, it should have something to do with G-CW complexes.