The Burnside ring and fusion systems

Antonio Diaz and Assaf Libman

Abstract: Given a saturated fusion system $\F$ on a finite $p$-group $S$ 
we show that after closing the ``centric orbit category'' $\O(\F^c)$ of 
$\F$ to coproducts, the resulting category is also closed to products 
and pullbacks. There results a ring $\A(\F)$ modeled on the Burnside 
ring $\A(G)$ of finite groups. We show that these rings have several 
properties in common. When $\F$ is the fusion system of $G$ we describe 
the relationship between these rings. Our results also set up a suitable 
framework to define and study Mackey functors for $\F$.