Checkbox in DataGridView will not change its value after validation

I have checkboxes in one of my columns in a DataGridView.

And now I have a problem: when I click once on the checkbox, it changes, but only visually, in the code, its value is still set to false. But if I click on the Checkbox and then somewhere else on my datagridview (or change its value manually in the code to true), it will change its value to true.

How can I make my checkbox change the value after one click? (it is annoying that checking the checkbox does not actually check it).

Thanks for any help.