  The reduced unitary Whitehead group SK1 of a graded division algebra equipped
with a unitary involution (i.e., an involution of the second kind) and graded
by a torsion-free abelian group is studied. It is shown that calculations in
the graded setting are much simpler than their nongraded counterparts. The
bridge to the non-graded case is established by proving that the unitary SK1 of
a tame valued division algebra wih a unitary involution over a henselian field
coincides with the unitary SK1 of its associated graded division algebra. As a
consequence, the graded approach allows us not only to recover results
available in the literature with substantially easier proofs, but also to
calculate the unitary SK1 for much wider classes of division algebras over
henselian fields.
