What does on the pitch here mean?
In a football game in the Qatar Stars League between Al-Shahania and Al-Khor on Friday, a strange incident occurred when Al-Shahinia goalkeeper Khalifa Al-Dosari bends down to his knees and kisses the feet of his father, in apology to inappropriate behavior he was involved in" on the pitch"

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It's talking about the location of the inappropriate behaviour. The 'pitch' is the field where the football match was played. It's a very common term in British English, e.g. football pitch', 'rugby pitch, 'cricket pitch' etc. or often people just say 'pitch; by itself. i believe in American English they would say 'field' instead.

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Thanks alot

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The pitch is the field, or surface, on which the game is played. "On the pitch" can be taken literally as "on the field" or "on the playing surface" or it can be taken to mean "during the game". "There was more violence on the pitch than on the terraces" could be taken either way. I think in this case "during a game" is the closest equivalent.