  We present the first part of an analysis aimed at introducing variables which
are suitable for constructing a space of quantum states for the Teleparallel
Equivalent of General Relativity via projective techniques - the space is meant
to be applied in a canonical quantization of the theory. We show that natural
configuration variables on the phase space of the theory can be used to
construct a space of quantum states which however possesses an undesired
property. We introduce then a family of new variables such that some elements
of the family can be applied to build a space of quantum states free of that
property.
