Is it permissible in Sharia to sell shares that one does not own on margin (short selling), with the expectation that their price will fall, then buying them back later at a lower price and returning them to the broker?

The default rule in transactions is permissibility, unless prohibited by Sharia, such as gharar (excessive uncertainty), darar (harm), jahalah (ignorance), ghabn (deception/unfair exploitation), and selling what one does not own. It is impermissible to purchase shares of companies that deal in riba (interest/usury) or produce unlawful goods. The type of transaction mentioned in the question is impermissible due to its inclusion of gharar and selling what is not owned. The prohibition becomes even more severe if the companies produce unlawful goods or deal in riba. The fact that they are in foreign countries does not justify this prohibition.