The Morel-Voevodsky motivic stable homotopy category SH(S) of a Noetherian scheme S of finite Krull dimension admits a closed symmetric monoidal structure, as Rick Jardine showed in his beautiful article "Motivic symmetric spectra". In particular, the endomorphisms of the unit in SH(S), usually called the motivic sphere spectrum over S, form a commutative ring. If S is the spectrum of a field F, this commutative ring is the Grothendieck-Witt ring of symmetric bilinear forms over F, as Morel's celebrated theorem says. Morel's theorem does much more; it identifies the whole Milnor-Witt K-theory of F (which contains the Grothendieck-Witt ring in degree zero) with the graded ring of maps from the motivic sphere spectrum to smash powers of the Tate circle over F. In my talk I will explain how to extend this identification to the ring of integers.