  Let X be a Hilbert bimodule over a C*-algebra A and $O_X= A \rtimes_X \Z$.
Using a finite section method we construct a sequence of completely positive
contractions factoring through matrix algebras over A which act on $s_{\xi}
s_{\eta}^*$ as Schur multipliers converging to the identity. This shows
immediately that for a finitely generated X the algebra $O_X$ inherits any
standard approximation property such as nuclearity, exactness, CBAP or OAP from
A. We generalise this to certain general Pimsner algebras by proving
semi-splitness of the Toeplitz extension under certain conditions and discuss
some examples.
