Thanks! So that was the problem..
Still, the results confuse me even more: I have to analyse the entire world, not just one section, so I chose the WGS_1984_Web_Mercator_Auxiliary_Sphere. When I click on a cell close to the equator it shows the proper area of about 3,000,000,000 (55km times 55km), but when I go far to the North the stated area increases about threefold...
But it should be the other way around, should it not? The grids become smaller in the North, so it should give me a smaller area.