  We construct an endomorphism of the Jiang-Su algebra $\mathcal{Z}$ which does
not admit a conditional expectation. This answers a question in the
testamentary homework by E. Kirchberg. As an application, it is shown that any
unital separable nuclear $\mathcal{Z}$-absorbing C*-algebra is
non-transportable in the Cuntz algebra $\mathcal{O}_2$.
