Construction of the motivic cellular spectrum ${\mathbf{KO}}^{geo}$ over $Spec(\mathbb{Z})$

Abstract

We construct a periodic motivic spectrum over $Spec(\mathbb{Z})$ which when pulled back to any scheme $S$ with $\frac{1}{2}\in \Gamma (S,{\mathcal{O}}_S)$ is the $H{P}^1-$spectrum constructed by Panin and Walter. This spectrum ${\mathbf{KO}}^{geo}$ is constructed using closed subschemes of the Grassmannians $Gr(r,n)$. Using this we show that ${\mathbf{KO}}^{geo}$ is cellular.

Adapted from the author's PhD thesis. Version accepted for publication