The \(C^*\) -Algebra of the Infinite Dihedral Group \(D_{\infty }\)

The infinite dihedral group \(D_{\infty }=\langle a, t\mid a^2=t^2=1\rangle \) is isomorphic to the free product \({\mathbb Z}_2\ast {\mathbb Z}_2\) . As the simplest nonabelian infinite group, it plays an important role in group theory as well as in several other areas of mathematics.