For non-commutative locally compact groups formula_8 the classical Pontryagin construction stops working for various reasons, in particular, because the characters don't always separate the points of formula_8, and the irreducible representations of formula_8 are not always one-dimensional. At the same time it is not clear how to introduce multiplication on the set of irreducible unitary representations of formula_8, and it is even not clear whether this set is a good choice for the role of the dual object for formula_8. So the problem of constructing duality in this situation requires complete rethinking.