  The technique for constructing conformally invariant theories within the
coset space construction is developed. It reproduces all consequences of the
conformal invariance and Lagrangians of widely-known conformal field theories.
The method of induced representations, which plays the key role in the
construction, allows to reveal a special role of the "Nambu-Goldstone fields"
for special conformal transformations. Namely, their dependence on the
coordinates turns out to be fixed by the symmetries. This results in the
appearance of the constraints on possible forms of Lagrangians, which ensure
that discrete symmetries are indeed symmetries of the theory.
