Resumen

I will discuss ring structures on the K-theory of the core of a graph C*-algebra that are compatible with tensor product of invertible bimodules ("line bundles"). For a suitable class of graphs, one can show that the K-theory is generated by invertible bimodules and the ring structure is that of a polynomial ring constructed from the adjacency matrix of E. Examples include quantum projective spaces and the quantum space parameterizing Penrose tilings. For the former algebra, as a corollary one recovers some identities that were previously proved by Arici, Brain and Landi by means of index pairing.