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 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 K CR ( C ∗ R (Λ , γ )) for several examples of higher-rank graphs Λ with involution.