I'm looking for a good reference for a proof of the homotopy invariance of cyclic (co)homology.
I'm following a refernce book by Joachim Cuntz, the proofs are ommited therein, or only shown in the case of the base field $\mathbb{k}$ being $\mathbb{C}$. With this he shows the more general "differentiable homotopy invariance".
Though I'm looking for a proof of simply its polynomial homotopy invariance (since that is applicable to any basefield of arb. characteristic).
Also, I'd prefer a referecnce working with the cyclic homology not defined in an $A_{\infty}$, or DG setting. Just the simple setting of the category of non-commutative algebras.
Thanks