Permutation-equivariant quantum K-theory II. Fixed point localization

Using projective spaces as examples of toric manifolds, we examine K-theoretic fixed point localization. On the one hand, we will see how the permutation-equivariant theory of the point target space emerges as a necessary ingredient. On the other hand, we will completely characterize the genus-0 permutation-equivariant quantum K-theory of the given toric manifold in terms of such theory for the point, and a certain recursion relation.