Egorov's theorem for transversally elliptic operators on foliated   manifolds and noncommutative geodesic flow
  The main result of the paper is Egorov's theorem for transversally elliptic operators on compact foliated manifolds. This theorem is applied to describe the noncommutative geodesic flow in noncommutative geometry of Riemannian foliations. 
Yuri A. Kordyukov