  This paper introduces the notion of fusion action system, an abstraction of
the $p$-local data of a finite group acting on a finite set. Fusion action
systems are closely connected with the theory of fusion systems; we detail the
relationship of this new definition to the existing literature.
  We also develop a theory of classifying spaces of fusion action systems,
analogous to the relationship between by $p$-local finite groups and fusion
systems. This allows us to discuss the covering space theory arising from a
group action in a fusion-theoretic context.
