There are members of the Orthodox Church that use the Latin Mass as their Order of Worship instead of the Greek Liturgy. It is very interesting to consider that members of the Orthodox Church consider the Latin Mass, the spiritual patrimony of the historic Latin Western Church as part of their patrimony, too. In some ways the proponents look at the history and horizons of Orthodoxy as not merely being Greek or “Eastern.” Most of will say that to be Orthodox is to use the Greek forms. One needs to know that in the Russian Orthodox Church Outside Russia (ROCOR) and the Antiochian Orthodox Church have a growing membership using the Latin Mass.
Here is a brief video, “The Orthodox West,” which documents their perspective and work.