The measure preserving and nonsingular transformations of the jump Lévy processes

Let $\xi(t)$, $t\in[0,1]$ be a jump Lévy process. By $\mathcal P_\xi$ we denote the law of $\xi$ in the Skorokhod space $\mathbb D[0,1]$. Under some nondegeneracy condition on the Lévy measure $\Lambda$ of the process we construct a group of a $\mathcal P_\xi$-preserving transformations of the space $\mathbb D[0,1]$.