Box Product of Mackey Functors in Terms of Modules

The box product of Mackey functors has been studied extensively in Lewis's notes. As shown in Thevenaz and Webb's paper, a Mackey functor may be identified with a module over a certain algebra, called the Mackey algebra. We aim at describing the box product, in the sense of Mackey algebra modules. For a cyclic $p$-group $G$, we recover a result from Mazur's thesis. We generalize it to a general finite group $G$ in this article.