K-theory for real k-graph C∗-algebras

We initiate the study of real $C^*$-algebras associated to higher-rank graphs $\Lambda$, with a focus on their $K$-theory. Following Kasparov and Evans, we identify spectral sequence which computes $\mathcal{CR}$ $K$-theory $C^*_{\mathbb R} (\Lambda, \gamma)$ for any involution $\gamma$ show that $E^2$ page this can be straightforwardly computed from combinatorial data $k$-graph $\Lambda$ $\gamma$. provide complete description $K^{CR}(C^*_{\mathbb R}(\Lambda, \gamma))$ several examples involution.