The Dade group of Mackey functors for p-groups

We introduce endo-permutation Mackey functors and the Mackey–Dade group of a p-group and study their basic properties. We exhibit relations between the Mackey–Dade group of a finite p-group P and the Dade groups of the Weyl groups of all subgroups of P  . As a result, we show that the Mackey–Dade group tensored with QQ over ZZ is the kernel of the linearization map for Mackey functors, introduced by the author.