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Olise scored a penalty in stoppage-time to make it 2-2.
The 75-year-old succeeds Frenchman Patrick Vieira, who was sacked last week after a poor run of form left the team three points above the relegation zone.
Arsenal crushed Crystal Palace 4-1 to go into the international break with a solid lead.
Palace are the only Premier League team without a win in 2023, having drawn five and lost six of their games.
The win moved City to 61 points after 27 games, two behind leaders Arsenal, who play Fulham on Sunday, and 12 ahead of third-placed Manchester United.
The clubs have until Monday to respond to the charges.
Nottingham Forest beat Southampton to move out of the relegation zone.
Reds striker Darwin Nunez sent off for a head-butt on his home debut.
Gabriel Martinelli scored the first goal before home defender Marc Guehi turned the ball into his own net late on at Selhurst Park.
Vieira was confronted by a fan as he was walking towards the away dressing room after the final whistle. The fan appeared to provoke Vieira, who then kicked him to the ground and had to be led away by other supporters.
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