  It has been well established that for symmetry protected topological systems,
the non-trivial topology prevents a real space representation using
exponentially localized Wannier wavefunctions (WFs) in all directions, unless
the protecting symmetry is sacrificed as an on-site transformation. This makes
it challenging to determine the symmetry of various physical observables
represented using such WFs. In this work, we propose a practical method for
overcoming such challenges using the Kane-Mele model as a concrete example. We
present a systematic procedure for diagnosing the symmetry of any observables,
as well as a method for constructing symmetric operators up to arbitrary
truncation accuracy.
