We construct a natural, tame action of the monoid of injective self-maps of the set of natural numbers on the homotopy groups of a symmetric spectrum. This extra algebraic structure allows a conceptual and uniform understanding of various phenomena related to –isomorphisms, semistability and the relationship between naive and true homotopy groups for symmetric spectra.
"On the homotopy groups of symmetric spectra." Geom. Topol. 12 (3) 1313 - 1344, 2008. https://doi.org/10.2140/gt.2008.12.1313