I am interested in calculating the rationalized algebraic K-Theory groups of the group ring of $\mathbb Z/n$, that is $K\_i(\mathbb Z[\mathbb Z/n])\otimes \mathbb{Q}$ for any natural number $n\geq 2$. What is known about the rationalized K-Theory of $\mathbb Z[\mathbb Z/n]$ for an arbitrary $n$? 



rationalized K-Theory of the group ring of finite cyclic groups
The rationalized K-theory of finite groups is known: Let $G$ be a finite group and $n \ge 2$. 
$$K\_n(\mathbb Z G)\otimes \mathbb Q =
\begin{cases}
\mathbb{Q}^r & n\equiv 1(4) \newline 
\mathbb{Q}^c & n\equiv 3(4) \newline 
0 & n \text{ even}
\end{cases}$$
where $r$ is the number of irreducible real representations of $G$ and $c$ of them are of complex type (see Theorem 2.2 [here](http://folk.uio.no/bjoernj/papers/kg.pdf)). 


Now let $G=\mathbb{Z}/n$. If $n$ is odd then $r=(n+1)/2$ and $c=(n-1)/2$. If $n$ is even, then $r=(n+2)/2$ and $c=(n-2)/2$. 


