Multiple Dedekind Zeta Values are Periods of Mixed Tate Motives

Recently, the author defined multiple Dedekind zeta values associated to a
number K field and a cone C. These object are number theoretic analogue of
multiple zeta values. We prove that every multiple Dedekind zeta value over
totally real number field is a period of a mixed Tate motive. The mixed
motive is defined over K in terms of a the Deligne-Mumford compactification
of the moduli space of curves of genus zero with n marked points.