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Let $(G,{\mathfrak I},N,S)$ be an affine topological Tits system, and let$\Gamma$ be a torsion free cocompact lattice in $G$. This article studies thecoinvariants $H_0(\Gamma; C(\Omega,{\mathbb Z}))$, where $\Omega$ is theFurstenberg boundary of $G$. It is shown that the class $[1]$ of the identityfunction in $H_0(\Gamma; C(\Omega,{\mathbb Z}))$ has finite order, withexplicit bounds for the order.  A similar statement applies to the $K_0$ group of the boundary crossedproduct $C^*$-algebra $C(\Omega)\rtimes\Gamma$. If the Tits system has type$\widetilde A_2$, exact computations are given, both for the crossed productalgebra and for the reduced group $C^*$-algebra.

Torsion in Boundary Coinvariants and K-Theory for Affine Buildings