Does a morphism which induces an isomorphism between Hochschild homology also induce an isomorphism between cyclic homology?

Question

In a 1998 paper by B. Keller, the author consider the following problem in Section 1.4: Let $k$ be a commutative ring and $X$ a scheme over $k$. We can consider the cyclic homology as well as the Hochschild homology of $X$. He then asked

"If a morphism of schemes induces an isomorphism in Hochschild homology, does it always induce an isomorphism in cyclic homology?"

In the paper the author mentioned that this problem was still open.

My question is: Is there any progress on the above problem now?