  We introduce a computationally tractable way to describe the $\mathbb
Z$-homotopy fixed points of a $C_{n}$-spectrum $E$, producing a genuine $C_{n}$
spectrum $E^{hn\mathbb Z}$ whose fixed and homotopy fixed points agree and are
the $\mathbb Z$-homotopy fixed points of $E$. These form a piece of a
contravariant functor from the divisor poset of $n$ to genuine $C_{n}$-spectra,
and when $E$ is an $N_{\infty}$-ring spectrum, this functor lifts to a functor
of $N_{\infty}$-ring spectra.
  For spectra like the Real Johnson--Wilson theories or the norms of Real
bordism, the slice spectral sequence provides a way to easily compute the
$RO(G)$-graded homotopy groups of the spectrum $E^{hn\mathbb Z}$, giving the
homotopy groups of the $\mathbb Z$-homotopy fixed points. For the more general
spectra in the contravariant functor, the slice spectral sequences interpolate
between the one for the norm of Real bordism and the especially simple $\mathbb
Z$-homotopy fixed point case, giving us a family of new tools to simplify slice
computations.
