Let X be a DM stack over a field k. We follow the definition in Laumon and Moret-Bailly's book, so that its diagonal is quasi-compact (and hence diagonal is of finite type). Then is the diagonal necessarily finite?
Edit: I meant to ask if the inertia $I\to X$ is finite. Recall that the inertia stack $I$ is defined to be the 2-fiber product of $X$ with $X$ over $X\times X,$ where the two maps $X\to X\times X$ are both the diagonal map. This question is equivalent (I think) to the following. Let $G\to S$ be an etale $S$-group scheme of finite type, where $S$ is a $k$-scheme of finite type. Then $G$ is finite over $S.$