  We show that if $X$ is a toric scheme over a regular commutative ring $k$
then the direct limit of the $K$-groups of $X$ taken over any infinite sequence
of nontrivial dilations is homotopy invariant. This theorem was previously
known for regular commutative rings containing a field. The affine case of our
result was conjectured by Gubeladze. We prove analogous results when $k$ is
replaced by an appropriate $K$-regular, not necessarily commutative
$k$-algebra.
