  A general formulation of the Boundary Quantum Inverse Scattering Method is
given which is applicable in cases where $R$-matrix solutions of the
Yang--Baxter equation do not have the property of crossing unitarity. Suitably
modified forms of the reflection equations are presented which permit the
construction of a family of commuting transfer matrices. As an example, we
apply the formalism to determine the most general solutions of the reflection
equations for a solution of the Yang-Baxter equation with underlying symmetry
given by the Drinfeld double $D(D_3)$ of the dihedral group $D_3$. This
$R$-matrix does not have the crossing unitarity property. In this manner we
derive integrable boundary conditions for an open chain model of interacting
non-abelian anyons.
