A theorem of J.-P. Serre states that any finite subgroup $F$ of an (injective) amalgam $G\_1 \*\_H G\_2$ is conjugate into one of the factors $G\_1$ or $G\_2$, that is, $F$ is a subgroup of a vertex stabilizer of the Bass--Serre tree.

Is the following generalization true?: Any finite subgroup $F$ of the colimit $G$ of a developable complex of groups (in the sense of Bridson--Haefliger) is conjugate into one of the vertex groups $G\_v$.

I am away on a trip and do not have my usual resources! A specific reference would be appreciated :)