Inducing native Mackey functors to biset functors

Abstract: In this paper, we describe the induction functor from the category of native Mackey functors to the category of biset functors for a finite group $G$ over an algebraically closed field $k$ of characteristic zero. We prove two applications of this description. As the first application, we exhibit that any projective biset functor over $k$ is induced from a (rational) virtual native Mackey functor. The second application is the explicit description of the projective indecomposable biset functors parameterized by simple groups.