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We study actions of higher rank lattices $\Gamma<G$ on hyperbolic spaces, andwe show that all such actions satisfying mild properties come from the rank-onefactors of $G$. In particular, all non-elementary actions on an unboundedhyperbolic space are of this type. Our results also apply to lattices inproducts of trees, so that for example Burger--Mozes groups have exactly twonon-elementary actions on a hyperbolic space, up to a natural equivalence.

Hyperbolic actions of higher-rank lattices come from rank-one factors