Infinite sums of unstable Adams operations and cobordism

The elements of the ring of bidegree (0, 0) additive unstable operations in complex KK-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 MUMU, 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 pp, the analogous result in the pp-local split setting is also proved.