  We are concerned with the issue of quantization of a scalar field in a
diffeomorphism invariant manner. We apply the method used in Loop Quantum
Gravity. It relies on the specific choice of scalar field variables referred to
as the polymer variables. The quantization, in our formulation, amounts to
introducing the `quantum' polymer *-star algebra and looking for positive
linear functionals, called states. The assumed in our paper homeomorphism
invariance allows to determine a complete class of the states. Except one, all
of them are new. In this letter we outline the main steps and conclusions, and
present the results: the GNS representations, characterization of those states
which lead to essentially self adjoint momentum operators (unbounded),
identification of the equivalence classes of the representations as well as of
the irreducible ones. The algebra and topology of the problem, the derivation,
all the technical details and more are contained in the paper-part II.
