I am trying to understand the K-theory for the $C^*-$algebra of the continuous functions on the torus. In particular I am interested on the $K_0-$group. I have read that the generators are two elements: the unit $[1]$ and the Bott Projection $[Bott]$. Unfortunately, I cannot find the definition of the Bott projection for the torus, I have only seen the definition of the Bott projection for $\mathbb{R}^2$. Can someone tell me the definition of this projection? Or can someone give me another generator (in terms of projections)? I thank you all for the attention and the help.