We present a model of Saturn's global auroral response to the solar wind as observed by simultaneous Hubble Space Telescope (HST) auroral images and Cassini upstream measurements of the solar wind taken during the month of January 2004. These observations show a direct correlation between solar wind dynamic pressure and (1) auroral brightening toward dawn local time, (2) an increase of rotational movement of auroral features to as much as 75% of the corotation speed, (3) the movement of the auroral oval to higher latitudes, and (4) an increase in the intensity of Saturn Kilometric Radiation (SKR). Our model, referred to as the centrifugal instability model, provides an alternative to the reconnection model of Cowley et al. (2004a, 2004b, 2005); we suggest the above observations result from Saturn's magnetosphere being a fast rotator. Since the torques on Saturn's outer magnetosphere are relatively low, its outer magnetosphere will tend to conserve angular momentum. When compressed on the dayside, the outer magnetosphere spins up to higher angular velocities, and when it expands, the outer magnetosphere spins down to lower angular velocities. This response occurs since Saturn's ionosphere is unable to enforce corotation. The outer boundary of the plasma sheet at L ~ 15 is identified as the primary source location for the auroral precipitating particles. Enhanced wave activity, which can precipitate the auroral producing particles, may be present at this boundary. If radial transport is dominated by centrifugally driven flux tube interchange motions, when the magnetosphere spins up, outward transport will increase, and the precipitating particles will move radially outward (since the radial gradient in electron energy flux is negative). This mechanism will cause the auroral oval to move to higher latitudes as observed. The Kelvin-Helmholtz instability may contribute to the enhanced emission along the dawn meridian, as observed by HST, via enhanced wave activity and corresponding charged particle precipitation.