  In this paper we introduce exotic twisted $\mathbb T$-equivariant K-theory of
loop space $LZ$ depending on the (typically non-flat) holonomy line bundle
${\mathcal L}^B$ on $LZ$ induced from a gerbe with connection $B$ on $Z$. We
also define exotic twisted $\mathbb T$-equivariant Chern character that maps
the exotic twisted $\mathbb T$-equivariant K-theory of $LZ$ into the exotic
twisted $\mathbb T$-equivariant cohomology as defined in an earlier paper of
ours, and which localises to twisted cohomology of $Z$.
