Unitary SK_1 for a Graded Division Ring and its Quotient Division Ring
  Let E be a graded division ring finite-dimensional over its center with torsion-free abelian grade group, and let q(E) be its quotient division ring. Let tau be a degree-preserving unitary involution on E. We prove that SK_1(E, tau) is isomorphic to SK_1(q(E), tau). 
A. R. Wadsworth and V. I. Yanchevskii
math.RA