As the scion of a Michigan family business, Dart Container, that has long dominated the polystyrene foam market (it also makes plastic Solo cups and other iconic food service products), Mr. Dart was born into a significant fortune. But he also had a talent for trading, making lucrative investments over the decades in financial firms, biotech companies, Russian public vouchers and steeply discounted sovereign debt in Greece and Argentina, among many other companies and countries. Some investments made him enemies. His yacht was armored to withstand torpedo fire, one of his two brothers, Tom, told Bloomberg News in 1995. When Kenneth Dart relocated to Grand Cayman, his secretiveness and colorful business dealings aroused local suspicion. In 1993, his home in Sarasota, Fla., burned to the ground in an arson that was never fully explained. After Mr. Dart renounced his ties to America a few months later, he moved first to Belize, whose government in 1995 proposed to the State Department a Belizean consulate in Sarasota, where Mr. Dart and his family could live, presumably tax-free. The idea was never seriously considered, and Mr. Dart settled on Grand Cayman. Many islanders take it for granted that he is the biggest private landholder on the islands, and some suspect he owns more land than the government. In addition to resorts, office buildings and residential properties, his company began planning and building major municipal infrastructure projects like tunnels and roads, reinvigorating long-held concerns on Grand Cayman that Mr. Dart and his subsidiaries controlled too much of the island. In 2014, Mr. Dart stepped down as president of his family’s container business and has, according to comments made in 2015 by the Dart Enterprises chief executive, Mark VanDevelde, become more focused on real-estate development and conservation. The company has invested more than $1.5 billion in the Cayman Islands, with another $1 billion in the development pipeline. This does not include the estimated price tag for the skyscraper. Bloomberg puts Mr. Dart’s net worth at $5.8 billion.