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The prediction and experimental verification of the quantum spin Hall state marked the discovery of a new state of matter now known as topological insulators. Two-dimensional topological insulators exhibit the quantum spin-Hall effect, characterized by gapless spin-polarized counter-propagating edge channels. Whereas the helical character of these edge channels is now well established, experimental confirmation that the transport in the edge channels is spin polarized is still outstanding. We report experiments on nanostructures fabricated from HgTe quantum wells with an inverted band structure, in which a split gate technique allows us to combine both quantum spin Hall and metallic spin Hall transport in a single device. In these devices, the quantum spin Hall effect can be used as a spin current injector and detector for the metallic spin Hall effect, and vice versa, allowing for an all-electrical detection of spin polarization. [ABSTRACT FROM AUTHOR]