On the comparison of two constructions of Witt vectors of non-commutative rings

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Let A be any associative ring, possibly non-commutative, and let p be a prime number. Let E(A) be the ring of p-typical Witt vectors as constructed by Cuntz and Deninger and W(A) be that constructed by Hesselholt. The goal of this paper is to answer the following question by Hesselholt: Is HH₀(E(A)) isomorphic to W(A)? We show that in the case p=2, there is no such isomorphism possible if one insists it to be compatible with the Verscheibung operator and the Teichmüller map.