  We prove that the genuine $C_{2^n}$-spectrum
$N_{C_{2}}^{C_{2^n}}MU_{\mathbb{R}}$ is cofree, for all $n$. Our proof is a
formal argument using chromatic hypercubes and the Slice Theorem of Hill,
Hopkins, and Ravenel. We show that this gives a new proof of the Segal
conjecture for $C_2$, independent of Lin's theorem.
