Simply press Tab after Alt+Down Arrow, E, to go to the checkbox list below the Search field.
Checks and unchecks items with the Space Bar.
To choose items, use the up and down arrows.
The last item is jumped to when the end button is pressed.
The cursor jumps to the first item in the list at home.
To go to the first/last item in the list, go to the top/bottom of the page.