Noncommutative Riesz Theorem and Weak Burnside Type Theorem on Twisted Conjugacy

The paper consists of two parts. In the first part, we prove a noncommutative analog 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 a Burnside type theorem on twisted conjugacy for arbitrary discrete groups.