We initiate the study of real C ∗-algebras associated to higher-rank graphs Λ, with a focus on their K-theory. Following Kasparov and Evans, we identify a spectral sequence which computes the CR K-theory of CR∗ (Λ, γ) for any involution γ on Λ, and show that the E 2 page of this spectral sequence can be straightforwardly computed from the combinatorial data of the k-graph Λ and the involution γ. We provide a complete description of KCR(CR∗ (Λ, γ)) for several examples of higher-rank graphs Λ with involution.
- Higher rank graphs
- Real C ∗-algebras