hollow chamber profile 5 the hollow chamber profile 5 is designed as a two chamber profile with two hollow chambers 33 u2032 and 33 u2033 in the case of such a hollow chamber profile 5 with two hollow chambers 33 u2032 and 33 u2033 it would be possible to fill the different hollow chambers 33 u2032 and 33 u2033 with different pressures this may be expedient for specific applications in order to optimize certain energy dissipation properties in the exemplary embodiment of fig9 in addition to the inner web 10 a further inner web 11 is arranged in the hollow chamber profile 5 said inner web 11 also serves primarily to reinforce the entire bumper arrangement if however this inner web 11 also passes completely through the hollow chamber profile 5 the hollow chamber profile 5 becomes a four chamber profile with four hollow chambers 33 u2032 33 u2033 33 u2032 u2033 and 33 u2033 u2033 it would also be possible in turn here to fill the different hollow chambers 33 u2032 33 u2033 33 u2032 u2033 and 33 u2033 u2033 with different pressures in the exemplary embodiment according to fig1 the crossmember 2 is now formed as a rectangle with an upper wall 31 and a lower wall 32 that connect the front wall 19 to the rear wall 20 of the crossmember 2 a cross sectionally circular hollow chamber profile 5 with a hollow chamber 33 is arranged within the crossmember 2 a further hollow chamber 35 is now also formed between the hollow chamber profile 5 and the upper wall 31 a further hollow chamber 34 is now also formed between the hollow.