Communicated by C.A. Weibel MSC:The elements of the ring of bidegree (0, 0) additive unstable operations in complex K -theory can be described explicitly as certain infinite sums of Adams operations. Here we show how to make sense of the same expressions for complex cobordism MU, thus identifying the ''Adams subring'' of the corresponding ring of cobordism operations. We prove that the Adams subring is the centre of the ring of bidegree (0, 0) additive unstable cobordism operations.For an odd prime p, the analogous result in the p-local split setting is also proved.

Abstract. This paper provides a unifying approach to recent results linking the fields of integer-valued polynomials and operations in K-theory. Following work of Bhargava, we set up a general framework encompassing several examples of rings of integer-valued polynomials. Our main results give bases for the duals of these rings. The rings and their duals all arise in topology as various kinds of cooperations and operations in complex K-theory. We show how several previously understood examples fit into this framework and we present some new examples.