  An example is given of a simple, unital C*-algebra which contains an infinite
and a non-zero finite projection. This C*-algebra is also an example of an
infinite simple C*-algebra which is not purely infinite. A corner of this
C*-algebra is a finite, simple, unital C*-algebra which is not stably finite.
  Our example shows that the type decomposition for von Neumann factors does
not carry over to simple C*-algebras.
  Added March 2002: We also give an example of a simple, separable, nuclear
C*-algebra in the UCT class which contains an infinite and a non-zero finite
projection. This nuclear C*-algebra arises as a crossed product of an inductive
limit of type I C*-algebras by an action of the integers.
