  The exotic bialgebra S03, defined by a solution of the Yang-Baxter equation,
which is not a deformation of the trivial, is considered. Its FRT dual algebra
$s03_F$ is studied. The Baxterisation of the dual algebra is given in two
different parametrisations. The finite-dimensional representations of $s03_F$
are considered. Diagonalisations of the braid matrices are used to yield
remarkable insights concerning representations of the L-algebra and to
formulate the fusion of finite-dimensional representations. Possible
applications are considered, in particular, an exotic eight-vertex model and an
integrable spin-chain model.
