On the hyperreal dual Steenrod algebra

Abstract

We compute the dual Steenrod algebra for Bredon homology with constant coefficients $\underline{\mathbb{Z}}$ and $\underline{\mathbb{Z}}/2$ 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 $H{\underline{\mathbb{F}}}_2\otimes H\underline{\mathbb{Z}}$.