The esports firm said it will oversee the delivery of the tournament, tournament operations and broadcast production for the series, which will be played every weekend in place of the F1 Grand Prix, which has been postponed due to the coronavirus outbreak.
The first race, the Virtual Bahrain Grand Prix, took place on 22 March and further races are scheduled to take place until May and will be extended if the pandemic results in further Grand Prix cancellations.
Gfinity added that each race is broadcast live from its Esports Arena in London and will be available on the official Formula 1 YouTube, Twitch and Facebook channels.
"We are excited to be involved in the delivery of the F1 Esports Virtual Grand Prix series. At Gfinity we are committed to delivering esports solutions for our partners and we are proud to be part of the series that will bring exciting entertainment based virtual racing to a legion of Formula 1 and gaming fans around the globe", said Gfinity chief executive John Clarke.
The shares surged 34% to 0.6p in early deals on Monday.
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