On Voevodsky's algebraic K-theory spectrum BGL

Under a certain normalization assumption we prove that the ${\text{Pro}}^1$-spectrum $\mathrm{B}\mathrm{G}\mathrm{L}$ of Voevodsky which represents algebraic $K$-theory is unique over $\text{Spec}(\mathbb{Z})$. Following an idea of Voevodsky, we equip the ${\text{Pro}}^1$-spectrum $\mathrm{B}\mathrm{G}\mathrm{L}$ with the structure of a commutative ${\text{Pro}}^1$-ring spectrum in the motivic stable homotopy category. Furthermore, we prove that under a certain normalization assumption this ring structure is unique over $\text{Spec}(\mathbb{Z})$. For an arbitrary Noetherian scheme $S$ of finite Krull dimension we pull this structure back to obtain a distinguished monoidal structure on $\mathrm{B}\mathrm{G}\mathrm{L}$. This monoidal structure is relevant for our proof of the motivic Conner-Floyd theorem. It has also been used by Gepner and Snaith to obtain a motivic version of Snaith’s theorem.