  Based on the treatment of the chiral Ising model by Mack and Schomerus, we
present examples of localized endomorphisms $\varrho_1^{\rm loc}$ and
$\varrho_{1/2}^{\rm loc}$. It is shown that they lead to the same
superselection sectors as the global ones in the sense that unitary equivalence
$\pi_0\circ\varrho_1^{\rm loc}\cong\pi_1$ and $\pi_0\circ\varrho_{1/2}^{\rm
loc}\cong\pi_{1/2}$ holds. Araki's formalism of the selfdual CAR algebra is
used for the proof. We prove local normality and extend representations and
localized endomorphisms to a global algebra of observables which is generated
by local von Neumann algebras on the punctured circle. In this framework, we
manifestly prove fusion rules and derive statistics operators.
