  For $\Gamma$ a relatively hyperbolic group, we construct a model for the
universal space among $\Gamma$-spaces with isotropy on the family VC of
virtually cyclic subgroups of $\Gamma$. We provide a recipe for identifying the
maximal infinite virtually cyclic subgroups of Coxeter groups which are
lattices in $O^+(n,1)= \iso(\mathbb H^n)$. We use the information we obtain to
explicitly compute the lower algebraic K-theory of the Coxeter group $\gt$ (a
non-uniform lattice in $O^+(3,1)$). Part of this computation involves
calculating certain Waldhausen Nil-groups for $\mathbb Z[D_2]$, $\mathbb
Z[D_3]$.
