In this talk we derive a novel and fundamental relation between C*-algebras and Complex Cobordism. We endow the space of complex genera with the structure of an infinite Lie group, with the underlying manifold being isomorphic to the group of automorphisms of the formal disc, and relate it then to operator algebras. The group operation introduced can be understood combinatorially in terms of planar rooted trees. Finally we shall give connections with Conformal Field Theory.