  We present a version of twisted equivariant $K$-theory-$K$-twisted
equivariant $K$-theory, and use Grothendieck differentials to compute the $K$
-twisted equivariant $K$-theory of simple simply connected Lie groups. We did
the calculation explicitly for SU(N) explicitly. The basic idea is to interpret
an equivariant gerbe as an element of equivariant $K$-theory of degree 1.
