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We introduce higher strip deformations, which give a way of constructingaffine deformations of discrete free groups in the image of the irreduciblerepresentation $\operatorname{PSL}_2\mathbb{R}\to \operatorname{SO}(2n,2n-1)$.We use the Margulis invariant to find a properness condition for thesedeformations, showing that each convex cocompact free group admits affinedeformations acting properly on $\mathbb{R}^{4n-1}$. Using our method we canalso construct proper affine actions of virtually free groups, which wedemonstrate by finding proper actions of $C_2 \star C_3$ on $\mathbb{R}^7.$

Constructing proper affine actions via higher strip deformations