  In this paper we give a definition of (centric) Mackey functor over a fusion
system which generalizes the notion of Mackey functor over a group. In this
context we prove that, given some conditions on a related ring, the centric
Burnside ring over a fusion system (as defined by Diaz and Libman) acts on any
centric Mackey functor. We also prove that the Green correspondence holds for
centric Mackey functors over fusion systems. As a means to prove this we
introduce a notion of relative projectivity for centric Mackey functors over
fusion systems and provide a decomposition of a particular product in
$\mathcal{O}\left(\mathcal{F}^c\right)_{\sqcup}$ in terms of the product in
$\mathcal{O}\left(N_{\mathcal{F}}\left(H\right)^c\right)_{\sqcup}$.
