  The reduced Whitehead group $\SK$ of a graded division algebra graded by a
torsion-free abelian group is studied. It is observed that the computations
here are much more straightforward than in the non-graded setting. Bridges to
the ungraded case are then established by the following two theorems: It is
proved that $\SK$ of a tame valued division algebra over a henselian field
coincides with $\SK$ of its associated graded division algebra. Furthermore, it
is shown that $\SK$ of a graded division algebra is isomorphic to $\SK$ of its
quotient division algebra. The first theorem gives the established formulas for
the reduced Whitehead group of certain valued division algebras in a unified
manner, whereas the latter theorem covers the stability of reduced Whitehead
groups, and also describes $\SK$ for generic abelian crossed products.
