The Eastern Ukraine is under the authority of the Patriarch of Moscow. Since the 1990s the Orthodox Church had spit into three churches, more over Politics then religion. This is addition to the split since 1576 with those Orthodox that agreed to being under the Pope (called "Uniate" Churches, not always as a complement, thus the tendency is NOT to use the word).
The Main Moscow Patriarch Orthodox is the Ukrainian Orthodox Church. While under the Patriarch of Moscow, it has "Autonomy" from Moscow, i.e. it is considered Independent of the Moscow Church but under the General Guidance of the Patriarch of Moscow. 50% of the population of the Ukraine belong to this branch of Christianity. It is considered in full Communion with the rest of world wide Orthodoxy. It is NOT self rule, i.e. a true " Autocephalous" Church, a church whose bishop report to no one higher. It still under the Patriarch of Moscow.
http://en.wikipedia.org/wiki/Ukrainian_Orthodox_Church_%28Moscow_Patriarchate%29
The second largest Church in the Ukraine if the Ukrainian Orthodox Church of the Kyivan Patriarch. 22% of Ukrainians report they belong to this church. It is NOT recognized by any other Orthodox Church, In 1992 the then leader of the above Ukrainian Orthodox Church tried to set up a true "Autocephalous" Ukrainian Church, but this was stopped when the Majority of the Orthodox Bishops of the Ukrainian said NO.
http://en.wikipedia.org/wiki/Ukrainian_Orthodox_Church_of_the_Kyivan_Patriarchate
The third group, broke with the Moscow Patriarch in 1921 and form their own independent "Autocephalous" Ukrainian Church. We have records of into the 1930s, then a revival during the German occupation, further suppression post WWII (and establishments of branched in the US and other Western Nations). In 1990 as the Soviet Union Broke up, it reappeared and today makes up about 10% of the Ukrainian population.
http://en.wikipedia.org/wiki/Ukrainian_Autocephalous_Orthodox_Church
Please note, when someone looked at the survey results that came up with the numbers of members in each of these churches, they notice some people put down a name of a branch they were NOT members of rather then name of the church they were members of. This appears to be the result of the some of the confusion between the above three Churches since 1990.
Lviv and the Western Ukraine tend to be what used to be called the "Uniate" Orthodox church, an Orthodox Church in tradition but under the Pope:
http://en.wikipedia.org/wiki/Ukrainian_Greek_Catholic_Church
The Ukrainian Greek Catholic Church, was founded when the Ukraine was under Catholic Polish rule in 1576. It remained a way for the Poles to control the Orthodox Ukrainians till the Partition of Poland in the 1700s. Those parts of the Ukraine under Russian Rule saw massive persecution of member of that church and pressure for them to join the Patriarch of Moscow. Most did.
That part of the Ukraine (Lviv and the surrounding area) came under Catholic Austria, Austria had also taken over large parts of Catholic Poland and decided it was better to keep these two "Catholic" Churches apart. Austria did this by improving the education of the Ukrainian Greek Catholic Church priests and in the process the Ukrainian Greek Catholic Church became the center of the growth of the concept known as being a "Ukrainian". When Austria loss this area to Poland at the end of WWI, Post WWI Poland continued that policy (Post WWII Poland tended to be lead by former Polish officers of the Austrian Imperial Army).
After WWII, Stalin had the Ukrainian Greek Catholic Church "agree" to join the Patriarch of Moscow, but most Ukrainian Greek Catholic Church member rejected this merger. When the Soviet Union dissolved, the Ukrainian Greek Catholic Church reemerged from the various underground places where it had been hiding. Today it is about 7-9% of the Population of the Ukraine, 50% in Lviv (Which has 1 Moscow Orthodox Church and Catholic Latin Churches).
http://www.catholic-hierarchy.org/diocese/dlviv.html
The biggest supporters of the War AGAINST Dombass is from these areas.
The official Name for this branch of the Catholic Church is "Ukrainian Catholic Church of the Byzantine Tradition". The second largest religion in Lviv is the Latin Rite Catholic Church then the Moscow Patriarch church.
I bring this up, for while most of the Ukrainians are Orthodox and admit to some relationship with the Patriarch of Moscow (or in the case of the Ukrainian Autocephalous Orthodox Church with the Patriarch of Constantinople), the "Ukrainian Catholic Church of the Byzantine Tradition" follows the guidance of the Pope. Thus Putin may want the Pope to put some pressure on the Western Ukrainians to step back and take a break and discuss the possibility of federating the Ukraine (Putin's preferred plan to solve the problems with the Ukraine). The Pope has some ability to get these radicals to at least discuss the concept of a Federation. The Pope can NOT ordered the Western Ukrainians to do so, but they will at least listen to him before saying NO.
In many ways Putin wants the Ukrainian problem solved, but not at the cost of abandoning his allies in the Eastern Ukraine. It is clear a deal has to be made, or this will fester for years and Putin is trying to cut a deal that both sides can live with.
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