The quotient conjecture for CAT(0) groups with rank-one elements

Let $G$ be a CAT(0) group, meaning a group acting geometrically on a CAT(0) space, and suppose that $G$ contains a rank-one element. Quotient conjecture. $G$ has a proper quotient with the same properties: it is a CAT(0) group with a rank-one element. The paper proves this possibility in the cubical setting, but the general case is stated as being out of reach with current technology and remains open.