  A paper by Haynes Miller shows that there is a filtration on the unitary
groups that splits in the stable homotopy category, where the stable summands
are certain Thom spaces over Grassmannians. We give an algebraic version of
this result in the context of Voevodsky's tensor triangulated category of
stable motivic complexes $\textbf{DM}(k,R)$, where $k$ is a field.
Specifically, we show that there are algebraic analogs of the Thom spaces
appearing in Miller's splitting that give rise to an analogous splitting of the
motive $M(\textrm{GL}_n)$ in $\textbf{DM}(k,R)$, where $\textrm{GL}_n$ is the
general linear group scheme over $k$.
