ESI The Erwin Schr

Noncommutative lattices have been recently used as nite topological approximations in quantum physical models. As a rst step in the construction of bundles and characteristic classes over such noncommutative spaces, we shall study their K-theory. We shall do it algebraically, by studying the algebraic K-theory of the associated algebras of`continuous functions' which turn out to be noncommutative approximately nite dimensional (AF) C-algebras. We also work out several examples.