  We study C*-algebras O_{\lambda} which arise in dynamics of the interval
exchange transformations and measured foliations on compact surfaces. Using
Koebe-Morse coding of geodesic lines, we establish a bijection between Bratteli
diagrams of such algebras and measured foliations. This approach allows us to
apply K-theory of operator algebras to prove strict ergodicity criterion and
Keane's conjecture for the interval exchange transformations.
