  Kashaev and Reshetikhin proposed a generalization of the Reshetikhin-Turaev
link invariant construction to tangles with a flat connection in a principal
G-bundle over the complement of the tangle. The purpose of this paper is to
adapt and renormalize their construction to define invariants of G-links using
the semi-cyclic representations of the non-restricted quantum group associated
to sl2, defined by De Concini and Kac. Our construction uses a modified Markov
trace. In our main example, the semi-cyclic invariants are a natural extension
of the generalized Alexander polynomial invariants defined by Akutsu, Deguchi,
and Ohtsuki. Surprisingly, direct computations suggest that these invariants
are actually equal.
