Noncommutative Riesz theorem and weak Burnside type theorem on twisted   conjugacy
  The present paper consists of two parts. In the first part, we prove a noncommutative analogue of the Riesz(-Markov-Kakutani) theorem on representation of functionals on an algebra of continuous functions by regular measures on the underlying space.   In the second part, using this result, we prove a weak version of Burnside type theorem for twisted conjugacy for arbitrary discrete groups. 
Evgenij Troitsky