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Let $\\alpha$ be a smooth $\\Gamma$-action on a compact nilmanifold $M$ that lifts to an action on the universal cover. If the linear data $\\rho$ of $\\alpha$ contains a hyperbolic element, then there is a continuous semiconjugacy intertwining the actions of $\\alpha$ and $\\rho$, on a finite-index subgroup of $\\Gamma$. 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