An apparatus for extracting exhaust air from a hob, the apparatus having an upper part, a fan duct connecting the upper part with a fan, and an exhaust air outlet, the upper part comprising: a frame including a hob opening for receiving a hob having standard dimensions and, on both sides next to the hob opening, an exhaust air inlet formed as an extraction slit, wherein each exhaust air inlet has a movable closure flap and each closure flap has two side guides guiding the closure flap during opening and closing and, in an open position of the closure flap, define side walls of an intake duct; a cleaning module associated with and communicating with the exhaust air inlet, which cleaning module provides an exhaust air duct and which exhaust air duct in the flow direction of the exhaust air comprises a guide plate, a baffle plate providing a first separating means, a filter providing a second separating means, and a drip tray for collecting the separated grease droplets, wherein the exhaust air duct has a flow cross-section which decreases towards the baffle plate and increases towards the filter by arranging the guide plate such that a distance (b) between a lower edge of the guide plate and a free edge of the baffle plate is approximately 60% of a distance (a) between the guide plate and the closure flap in an upper region of the exhaust air duct, so that the baffle plate arranged for deflecting the exhaust air at an angle of approximately 20° with respect to the horizontal, is supplied with an accelerated exhaust air flow due to the reduction of the flow cross-section, and the vertically arranged filter is supplied with a slowed down exhaust air flow due to the increase of the flow cross-section. a frame including a hob opening for receiving a hob having standard dimensions and, on both sides next to the hob opening, an exhaust air inlet formed as an extraction slit, wherein each exhaust air inlet has a movable closure flap and each closure flap has two side guides guiding the closure flap during opening and closing and, in an open position of the closure flap, define side walls of an intake duct; a cleaning module associated with and communicating with the exhaust air inlet, which cleaning module provides an exhaust air duct and which exhaust air duct in the flow direction of the exhaust air comprises a guide plate, a baffle plate providing a first separating means, a filter providing a second separating means, and a drip tray for collecting the separated grease droplets, wherein the exhaust air duct has a flow cross-section which decreases towards the baffle plate and increases towards the filter by arranging the guide plate such that a distance (b) between a lower edge of the guide plate and a free edge of the baffle plate is approximately 60% of a distance (a) between the guide plate and the closure flap in an upper region of the exhaust air duct, so that the baffle plate arranged for deflecting the exhaust air at an angle of approximately 20° with respect to the horizontal, is supplied with an accelerated exhaust air flow due to the reduction of the flow cross-section, and the vertically arranged filter is supplied with a slowed down exhaust air flow due to the increase of the flow cross-section. the exhaust air duct has a flow cross-section which decreases towards the baffle plate and increases towards the filter by arranging the guide plate such that a distance (b) between a lower edge of the guide plate and a free edge of the baffle plate is approximately 60% of a distance (a) between the guide plate and the closure flap in an upper region of the exhaust air duct, so that the baffle plate arranged for deflecting the exhaust air at an angle of approximately 20° with respect to the horizontal, is supplied with an accelerated exhaust air flow due to the reduction of the flow cross-section, and the vertically arranged filter is supplied with a slowed down exhaust air flow due to the increase of the flow cross-section.