Noncommutative Generalization of Wilson Lines
  A classical Wilson line is a cooresponedce between closed paths and elemets of a gauge group. However the noncommutative geometry does not have closed paths. But noncommutative geometry have good generalizations of both: the covering projection, and the group of covering transformations. These notions are used for a construction of noncommutative Wilson lines. Wilson lines can also be constructed as global pure gauge fields on the universal covering space. The noncommutative analog of this construction is also developed. 
Petr Ivankov
math.OA