The structure of $C^*$-subalgebras of the Toeplitz algebra fixed with respect to a finite group of automorphisms

In this paper we study the $C^*$-subalgebras of the Toeplitz algebra $\mathcal T$, each element of which is fixed relative to finite subgroup of automorphisms of the algebra $\mathcal T$. We prove that such subalgebras have a finite family of unitarily equivalent irreducible representations.