We construct a periodic motivic spectrum over Spec(Z) which when pulled back to any scheme S with 1/2∈Γ(S,O_S) is the HP¹-spectrum constructed by Panin and Walter. This spectrum KO^geo is constructed using closed subschemes of the Grassmannians Gr(r,n). Using this we show that KO^geo is cellular.

The author would like to thank Universität Osnabrück for the opportunity to complete their PhD as part of the Institute of Mathematics and providing support as part of the graduate school "DFG-GK1916 Combinatorial Structures in Geometry".