  Recently, the author defined multiple Dedekind zeta values [5] associated to
a number K field and a cone C. These objects are number theoretic analogues of
multiple zeta values. In this paper we prove that every multiple Dedekind zeta
value over any number field K is a period of a mixed Tate motive. Moreover, if
K is a totally real number field, then we can choose a cone C so that every
multiple Dedekind zeta associated to the pair (K;C) is unramified over the ring
of algebraic integers in K. In [7], the author proves similar statements in the
special case of a real quadratic fields for a particular type of a multiple
Dedekind zeta values. The mixed motives are defined over K in terms of a the
Deligne-Mumford compactification of the moduli space of curves of genus zero
with n marked points.
