  We study certain formal group laws equipped with an action of the cyclic
group of order a power of $2$. We construct $C_{2^n}$-equivariant Real oriented
models of Lubin-Tate spectra $E_h$ at heights $h=2^{n-1}m$ and give explicit
formulas of the $C_{2^n}$-action on their coefficient rings. Our construction
utilizes equivariant formal group laws associated with the norms of the Real
bordism theory $MU_{\mathbb{R}}$, and our work examines the height of the
formal group laws of the Hill-Hopkins-Ravenel norms of $MU_{\mathbb{R}}$.
