Proposition 2

Every composition operator of order 0 is invertible in the algebra $\Gamma$ of composition operators on $\mathbf{K}[X]$.

Indeed, a formal series $\sum_{k=0}^{\infty} \alpha_k S^k$ such that $\alpha_0 \neq 0$ is invertible in the ring $\mathbf{K}[[S]]$ (Alg., IV. 41); the proposition thus follows from th. 1 of VI, p. 271.