  Motivated by the splitting principle, we define certain simplicial complexes
associated to an associative ring $A$, which have an action of the general
linear group $GL(A)$. This leads to an exact sequence, involving Quillen's
algebraic K-groups of $A$ and the symbol map. Computations in low degrees lead
to another view on Suslin's theorem on the Bloch group, and perhaps show a way
towards possible generalizations.
