The nonsingular transformations of the tempering stable Lévy processes

Let $\xi(t)$, $t\in[0,1]$ be a tempering stable process. By $\mathcal P_\xi$ we denote the law of $\xi$ in the Skorokhod space $\mathbb D[0,1]$. For the measure $\mathcal P_\xi$ we construct the group of nonsingular transformations of $\mathbb D [0,1]$.