Galois Deformation Rings and Base Change to a Quadratic Field

Fix a prime p>3 and consider the universal 2-dimensional minimal p-ordinary deformation with coefficients in the universal ring T, of a modulo  p  induced representation r from a quadratic field F. The twist by the quadratic character of  F  induces an involution i on T.  We describe the fixed subring T_+   as the universal minimal pseudo-character ring deforming the restriction of Tr(r) to the Galois group over  F.