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But yes, I don't know in how far ten Hag is involved in transfer decisions and whether he has a lot to say in the club when it comes to player transfers, but there have been some questionable decisions in the recent past.
I don't think he is entirely to blame for Manchester United's poor form. In the past they have spent millions of dollars on players like Jadon Sancho, Harry Maguire and Anthony Martial and they have never benefited from them. So, there is a long history of bad and wrong transfer policy at Manchester United. They are like Chelsea, but not as bad as Chelsea.

I don't think Erik ten Hag has a squad that can compete with his rivals. Manchester United need a lot of transfers and they have almost no chance of winning the Champions League.
Ten hag is very much involved and have a great influence on transfer decision in Manchester united, at the end of last season he was given good amount of money to get players for the team, according to speculations he was given a 100% authority on decision as it regards transfer so he could get the best players he knows he can work with and achieve a good result for the team.
I think ten hag has the full blame when it comes to transfer errors because he was allowed to make choices for the team but sadly his choices has not been able to favour the team enough, or maybe are they new player yet to get used to the teams style and the environment? I really don't think because they have gotten more than enough time to do that already so it's expected by now they have gone passed that stage.
Onana is one of his worse transfer error he did this season, even Maguire hasn't been the best compared to when he was still in his formal team, Martial has even performed better when he was still in Chelsea than he has been in old Trafford, almost all the new signed players are still glorified in the past they are yet to prove something spectacular for the present and Manchester united did spent heavily on them.