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

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 in [1] and W(A) be that constructed by Hesselholt in [3]. The goal of this paper is to answer the following question by Hesselholt: Is HH0(E(A))≅W(A)? We show that in the case p=2, there is no such isomorphism possible if one insists that it be compatible with the Verschiebung operator and the Teichmüller map.