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Let E be a graded division ring finite-dimensional over its center withtorsion-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).

Unitary SK_1 for a Graded Division Ring and its Quotient Division Ring