K-theory for real k-graph C∗-algebras

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 C^*R (Λ, γ) for any involution $γ$ on $Λ$, and show that the E² 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(C^*R(Λ, γ)) for several examples of higher-rank graphs $Λ$ with involution.