The circumstellar disk of AB Aurigae has garnered strong attention owing to the apparent existence of spirals at a relatively young stage and also the asymmetric disk traced in thermal dust emission. However, the physical conditions of the spirals are still not well understood. The origin of the asymmetric thermal emission is unclear. We observed the disk at 230 GHz (1.3 mm) in both the continuum and the spectral line ^12CO J=2-1 with IRAM 30-m, the Plateau de Bure interferometer, and the Submillimeter Array to sample all spatial scales from 0.37 to about 50. To combine the data obtained from these telescopes, several methods and calibration issues were checked and discussed. The 1.3 mm continuum (dust) emission is resolved into inner disk and outer ring. Molecular gas at high velocities traced by the CO line is detected next to the stellar location. The inclination angle of the disk is found to decrease toward the center. On a larger scale, based on the intensity weighted dispersion and the integrated intensity map of ^12CO J=2-1, four spirals are identified, where two of them are also detected in the near infrared. The total gas mass of the 4 spirals (M_spiral) is 10^-7 < M_spiral < 10^-5 M_sun, which is 3 orders of magnitude smaller than the mass of the gas ring. Surprisingly, the CO gas inside the spiral is apparently counter-rotating with respect to the CO disk, and it only exhibits small radial motion. The wide gap, the warped disk, and the asymmetric dust ring suggest that there is an undetected companion with a mass of 0.03 M_sun at a radius of 45 AU. Although an hypothetical fly-by cannot be ruled out, the most likely explanation of the AB Aurigae system may be inhomogeneous accretion well above or below the main disk plane from the remnant envelope, which can explain both the rotation and large-scale motions detected with the 30-m image.