I will describe a work in progress, joint with Bai, Juran,
and Riedel, constructing a Fourier transform for the motivic spectrum
representing algebraic K-theory. Applying this to algebraic tori, this
gives a spectral level, multiplicative description of the K-theory of
(not necessarily split) tori, allowing to recover and extend the
computation of their Grothendieck $K_0$ group by Merkurjev-Panin.