On the hyperreal dual Steenrod algebra

We compute the dual Steenrod algebra for Bredon homology with constant coefficients $\underset{‾}{\mathbb{Z}}$ and $\underset{‾}{\mathbb{Z}}\mathrm{/}2$ in the category of modules over $M{U}^{((G))}$, the norm to $G=C_{2^n}$ of $M{U}_{\mathbb{R}}$. Using this and an equivariant version of the Greenlees–Serre spectral sequence, we give a spectral sequence computing the $RO$-graded homotopy of the Eilenberg–Mac Lane spectrum $H{\underset{‾}{\mathbb{F}}}_2\otimes H\underset{‾}{\mathbb{Z}}$.