Question: I'd like to extend the I2C bus. Is there something like a repeater for I2C?

Yes indeed this exists. Philips manufactures a special chip to buffer the bi-directional lines of the I2C bus. Typically, this is a current amplifier. It forces current into the wiring (a couple of mA). That way you can overcome the capacitance of long wiring.

However, you will need this component on both sides of the line. The charge pump in this devices can deliver currents up to 30mA which is way too much for a normal I2C chip to handle. With these buffers you can handle loads up to 2nF. The charge amplifier 'transforms' this load down to a 200pF load which is still acceptable by I2C components.