As the head of the company, Hayward became a lightning rod for public and political anger after the drill rig operated by BP exploded in the Gulf of Mexico in April.
Earlier this year, the head of the Asian football associations warned that powerful illegal betting syndicates in the region could attempt to rig World Cup finals games by bribing players or referees.
Mr Tshisekedi has also alleged that the head of the national election commission favoured Mr Kabila, and that "ghost" polling stations would be used to rig the result.