The Hochschild—Kostant—Rosenberg (HKR) theorem gives an isomorphism between Hochschild homology of an algebra $A$, an algebraic invariant, and its module of Kahler differentials, a geometric invariant. What happens when the algebra in question has an action by a finite group? Does this isomorphism respect the group action? Does that question even make sense? These questions will be used as an excuse to introduce some wacky objects called Mackey functors and explore their algebra.

(Less background required than you might think!)