Twisted topological Hochschild homology of Cn-equivariant spectra was introduced by Angeltveit, Blumberg, Gerhardt, Hill, Lawson, and Mandell, building on the work Hopkins, Ravenel norms in equivariant homotopy theory. In this paper we introduce tools for computing twisted THH, which apply to computations Thom spectra, Eilenberg-MacLane real bordism spectrum MUR. particular, construct an versio...