MOSCOW—President Vladimir Putin inspected a prototype of a new Sukhoi fifth-generation fighter jet on Tuesday that Russia unveiled at its annual MAKS air show with an eye on export markets. The warplane, given the project name “Checkmate,” is likely to be touted as a rival to the U.S. F-35 stealth fighter, said Oleg Panteleyev, head of the Aviaport analytical agency. The warplane is expected to fly its first maiden voyage in 2023 with a first batch due to be produced in 2026, the Interfax news agency cited a presentation as saying. Rostec, Russia’s state aerospace and defense conglomerate, said the plane was hard to detect and would have low operating costs. A brief promotional video featured pilots from UAE, India, Vietnam, and Argentina, suggesting that Moscow wants to pitch the plane overseas. Russia has successfully produced prototypes of new weapons systems in recent years, but has sometimes struggled to move …