  We provide a purely local computation of the (elliptic) twisted (by
"transpose-inverse") character of the representation \pi=I(\1) of PGL(3) over a
p-adic field induced from the trivial representation of the maximal parabolic
subgroup. This computation is independent of the theory of the symmetric square
lifting of [IV] of automorphic and admissible representations of SL(2) to
PGL(3). It leads to a proof of the (unstable) fundamental lemma in the theory
of the symmetric square lifting, namely that corresponding spherical functions
(on PGL(2) and PGL(3)) are matching: they have matching orbital integrals.
