A Ukrainian bank sued former owner Igor Kolomoisky in Delaware, saying the exiled billionaire acquired hundreds of millions of dollars in U.S. assets by laundering money from improper loans.

PrivatBank officials claim Kolomoisky and others used wrongfully issued loans to acquire commercial real estate through a network of companies in Delaware and Ohio, according to the lawsuit filed May 20 in Delaware Chancery Court. At one point, the companies were the largest holders of commercial properties in Cleveland, the suit...