Some inverse limits of Cuntz algebras
  We construct a nontrivial inverse system of Cuntz algebras $\{{\cal O}_{n}:2\leq n<\infty\}$, whose inverse limit is *-isomorphic onto ${\cal O}_{\infty}$. By using this result, it is shown that the $K_{0}$-functor is discontinuous with respect to the inverse limit even if the limit is a C$^{*}$-algebra. 
Katsunori Kawamura
math.OA math.KT