On up to date massively parallel computers domain decomposition approaches possess the advantage of a high computation/communication and/or computation/memory access ratio, especially when compared to traditional point-wise iterative schemes. Thus it suggests itself to use such block iterative methods with overlapping or non-overlapping blocks as well as smoothers in multigrid methods. However, numerical results show evidence that these block smoothers are not as efficient as expected when standard coarsening procedures are in effect. In order to fully benefit from block smoothers we thus propose a different coarsening scheme and an associated new local interpolation for the usage of block smoothers in multigrid methods. Using this scheme, we obtain textbook multigrid efficiency with fast convergence rate albeit we are able to coarsen very aggressively. Using this scheme we are able to benefit from the large amount of work that can be moved to solving the block systems locally in the block smoother on one hand and on the other hand reduce the global part of computations by allowing for very aggressive coarsening. In this talk, we present the resulting method in detail, give an overview over the theoretical analysis, show numerical results and give an outlook on possible extensions of the method from an geometric-algebraic to a completely algebraic context.