On the Existence of Slices for Actions of Non-Compact Lie Groups

Summary:Let $\mathcal{G} \rightrightarrows M$ be a source locally trivial proper Lie groupoid such that each orbit is of finite type. The orbit projection $M \to M/\mathcal{G}$ is a fibration if and only if $\mathcal{G}\rightrightarrows M$ is regular