  We introduce a general class of automorphisms of rotation algebras, the
noncommutative Furstenberg transformations. We prove that fully irrational
noncommutative Furstenberg transformations have the tracial Rokhlin property,
which is a strong form of outerness. We conclude that crossed products by these
automorphisms have stable rank one, real rank zero, and order on projections
determined by traces (Blackadar's Second Fundamental Comparability Question).
  We also prove that several classes of simple quotients of the C*-algebras of
discrete subgroups of five dimensional nilpotent Lie groups, considered by
Milnes and Walters, are crossed products of simple C*-algebras (C*-algebras of
minimal ordinary Furstenberg transformations) by automorphisms which have the
tracial Rokhlin property. It follows that these algebras also have stable rank
one, real rank zero, and order on projections determined by traces.
