report on work in progress, joint with paul arne oestvaer. \\ \\ a cellular motivic invariant is a special type of functor from the category of commutative rings (or the opposite of schemes, say) to spectra. examples include algebraic k-theory, motivic cohomology, \'e{}tale cohomology and algebraic cobordism. dwyer-friedlander observed that for 2-adic \'e{}tale k-theory and certain related invariants, the value on z[1/2] can be described in terms of a fiber square involving the values on the real numbers, the complex numbers, and the field with three elements. \\ \\ i will explain a generalization of this result to arbitrary 2-adic cellular motivic invariants. as an application, we show that $\pi_0$ of the motivic sphere spectrum over z[1/2] is given by the grothendieck-witt ring of z[1/2], up to odd torsion.