It is my understanding that if a person owns an item, that item may not be taken outside of his Techum Shabbos (2,000 Amos) on Shabbos (e.g. Shulchan Aruch Orach Chayyim 397:3).
For example, if Reuven is in Israel and owns a necktie back at home, Shimon may not take it outside - as he is not allowed to remove the tie from Reuven's Techum Shabbos.
My question is what happens if it is already a time where Shabbos is over in Israel? Do we say that for Reuven it is no longer Shabbos, so Shimon may then take the necktie outside? Or do we go after the item?
In short: if it is no longer Shabbos for an item's owner, may that item be taken outside of it's owner's Techum?