The infinite tensor product
A = ⊗(Ai,pi) of a family of C∗-algebras Ai with respect to projections pi∈ Ai is
examined. The primitive ideal space and the characters of A are completely described
in the case where each Ai is simple, or separable and nuclear. If A is not type I, an
explicit construction is given of a factor representation of A generating an arbitrary
hyperfinite factor. In addition, new results are obtained about primitive
ideals and characters of a tensor product of two C∗-algebras. Examples are
given of various phenomena, providing solutions to previously published
problems.
