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Topological quivers generalize the notion of directed graphs in which thesets of vertices and edges are locally compact (second countable) Hausdorffspaces. Associated to a topological quiver $Q$ is a $C^*$-correspondence, andin turn, a Cuntz-Pimsner algebra $C^*(Q).$ Given $\Gamma$ a locally compactgroup and $\alpha$ and $\beta$ endomorphisms on $\Gamma,$ one may construct atopological quiver $Q_{\alpha,\beta}(\Gamma)$ with vertex set $\Gamma,$ andedge set $\Omega_{\alpha,\beta}(\Gamma)= \{(x,y)\in\Gamma\times\Gamma\st\alpha(y)=\beta(x)\}.$ In \cite{Mc1}, the author examined the Cuntz-Pimsneralgebra $\cO_{\alpha,\beta}(\Gamma):=C^*(Q_{\alpha,\beta}(\Gamma))$ and foundgenerators (and their relations) of $\cO_{\alpha,\beta}(\Gamma).$ In thispaper, the author uses this information to create a six term exact sequence inorder to calculate the $K$-groups of $\cO_{\alpha,\beta}(\Gamma).$

C*-algebras associated with topological group quivers II: K-groups