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Rota is not around anymore, so we can't go and ask him what he meant. My guess is that he is referring to the $\lambda$-ring structure of symmetric functions which is related to plethysm and the composition of Schur functors (that's the representation theory connection as well as the category theoretic one regarding polynomial functors). This $\lambda$-ring structure plays a role in $K$-theory as explained, e.g. see "Riemann-Roch Algebra" by Fulton and Lang. Donald Yau's "Lambda-Rings" book and this long survey article about big Witt vectors by Hazewinkel are also nice (and probably more accessible) pedagogical references.