Dirac type operators on the quantum solid torus with global boundary   conditions
  We define a noncommutative space we call the quantum solid torus. It is an example of a noncommutative manifold with a noncommutative boundary. We study quantum Dirac type operators subject to Atiyah-Patodi-Singer like boundary conditions on the quantum solid torus. We show that such operators have compact inverse, which means that the corresponding boundary value problem is elliptic. 
Slawomir Klimek and Matt McBride
math.OA