I would like to create a document with nonstandard quotation environment.

The goal is that on odd pages quotations have to be indent on the left, and on even pages in opposite way (indent on the right).
EDIT:
The Thomas F. Sturm's solution works well, but there is a problem with footnotes inside the myquotation box (see my question). Do you have another idea how to solve this task?

csquotesbe preferred here? – pluton Jul 16 '13 at 14:00csquoteshas such a feature. It has a lot of features, but I could not find this one on a quick scan over the documentation. – Thomas F. Sturm Jul 16 '13 at 14:34\vsplitis working and currently I see no automated way to get it controlling widows and orphans. – Thomas F. Sturm Jul 17 '13 at 08:08