  We discuss a finite-plasticity model based on the symmetric tensor $P^T P$
instead of the classical plastic strain $P$. Such a model structure arises from
assuming that the material behavior is invariant with respect to frame
transformations of the intermediate configuration. The resulting variational
model is lower-dimensional, symmetric, and based solely on the reference
configuration. We discuss the existence of energetic solutions both at the
material-point level and for the quasistatic boundary-value problem. These
solutions are constructed as limits of time discretizations. Eventually, the
linearization of the model for small deformations is ascertained via a rigorous
evolutive-$\Gamma$-convergence argument.
