The Cuntz algebra $O\_n$ is the C\*-algebra generated by n isometries $S\_1$, ..., $S\_n$ such that $S\_i^\* S\_j=\delta\_{i,j}$ and $\sum\_{i=1}^nS\_iS\_i^\*=1$. Cuntz proved that this algebra has the following K-theory: $K\_0(O\_n)=\mathbb{Z}\_{n-1}$, $K\_1(O\_n)=0$. Does any one know what are the generators of $K\_0(O\_n)$ ($n\geq 3$)? 



Generators K-theory of Cuntz algebras
This is answered on the first page of Cuntz's paper "K-Theory for Certain C\*-Algebras" (*Ann. of Math.* **113** (1981), 181-197). If you google "cuntz algebra k-theory" it is the first result.


