Royden's Theorem for free products

Let $G$ be a group which splits as $G = F_n * G_1 *...*G_k$, where every $G_i$ is freely indecomposable and not isomorphic to the group of integers.  Guirardel and Levitt generalised the Culler- Vogtmann Outer space of a free group by introducing an Outer space for $G$ as above, on which $\text{Out}(G)$ acts by isometries. Francaviglia and Martino introduced the Lipschitz metric for the Culler- Vogtmann space and later for the general Outer space. In a joint paper with Francaviglia and Martino, we prove that the group of isometries of the Outer space corresponding to $G$ , with respect to the Lipschitz metric, is exactly $\text{Out}(G)$. In this talk, we will describe the construction of the general Outer space and the corresponding Lipschitz metric in order to present the result about the isometries.