"Smith theory" is the name given to the investigation (starting with the work of P.A. Smith in the late 1930s) of the homological properties of the fixed-sets for finite groups (especially $p$-groups) acting on spheres. See Dwyer, William G., and Clarence W. Wilkerson. “Smith Theory Revisited.” The Annals of Mathematics 127, no. 1. Second Series (January 1988): 191-198.

Ian Hambleton and his student Lucian Savin have just posted an article about a coarse-geometric counterpart of Smith Theory, Hambleton, Ian, and Lucian Savin. “Coarse Geometry and P. A. Smith Theory.” 1007.0495 (July 3, 2010). http://arxiv.org/abs/1007.0495.

The notion of fixed set is replaced by a "coarse fixed set", which is the coarse structure (if it stabilizes) of the sequence of "approximate fixed sets" $\{x: d(x,f(x))\le n\}$ for $n=1,2,\ldots$.

This notion is well behaved for finite group actions.

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