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We prove that a GIT chamber quotient of an affine variety $X=Spec(A)$ by areductive group $G$, where $A$ is an almost factorial domain, is a Mori dreamspace if it is projective, regardless of the codimension of the unstable locus.This includes an explicit description of the Picard number, the pseudoeffectivecone, and the Mori chambers in terms of GIT. We apply the results to quivermoduli, to show that they are Mori dream spaces if the quiver contains nooriented cycles, and if stability and semistability coincide. We give a formulafor the Picard number in quiver terms. As a second application we prove thatgeometric quotients of Mori dream spaces are Mori dream spaces as well, whichagain includes a description of the Picard number and the Mori chambers. Someexamples are given to illustrate the results.

Quotients of spectra of almost factorial domains and Mori dream spaces