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We develop an adaptive receiver for multiple-input multiple-output (MIMO) frequency selective channels that employ space-time block-coded transmissions with cyclic prefixing. The receiver performs both interference suppression and equalization for multiuser transmissions. The structure of the space-time code is exploited to show that the receiver can be implemented on a per-frequency-bin basis rather than on a block-by-block basis. The adaptation scheme requires solving N independent problems each of complexity O(M2) per block iteration, where M is the number of users and N is the block size.