Let \(G\) be a discrete group and \(A\) be a \(C^*\text{-algebra}\). An action of \(G\) on \(A\nothing\) is a group homomorphism \(\alpha\) from \(G\) into the group of \(*-\text{automorphisms}\) on \(A\). A \(C^*\text{-algebra}\) equipped with a \(G\)-action is called a \(G\)-\(C^*\text{-algebra}\).