We present a {\em linear realizability} technique for building
{\em Partial Equivalence Relations (PER)} categories over 
{\em Linear Combinatory Algebras}. 
These PER categories turn out to be {\em linear categories} and 
to form an {\em adjoint model} with their {\em co-Kleisli categories}. 
We show that a special linear combinatory algebra of {\em partial 
involutions}, arising from {\em Geometry of Interaction} constructions,
gives rise to a {\em fully} and {\em.faithfully complete} model for 
{\em ML polymorphic types} of system F.
\\ {\bf Keywords:} ML-polymorphic types, linear logic, PER models, 
Geometry of Interaction, full completeness.