K-theory for real k-graph C*-algebras

We initiate the study of real C*-algebras associated to higher-rank graphs 3, 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)(Lambda,gamma) for any involution. on 3, and show that the E-2 page of this spectral sequence can be straightforwardly computed from the combinatorial data of the k-graph 3 and the involution gamma. We provide a complete description of K-CR(C*(R)(Lambda,gamma)) for several examples of higher-rank graphs Lambda with involution.