  We show that the abelian monoid of isomorphism classes of G-stable finite
S-sets is free for a finite group G with Sylow p-subgroup S; here a finite
S-set is called G-stable if it has isomorphic restrictions to G-conjugate
subgroups of S. These G-stable S-sets are of interest, e.g., in homotopy
theory. We prove freeness by constructing an explicit (but somewhat
non-obvious) basis, whose elements are in one-to-one correspondence with the
G-conjugacy classes of subgroups in S. As a central tool of independent
interest, we give a detailed description of the embedding of the Burnside ring
for a saturated fusion system into its associated ghost ring.
