You can use the Cinema 4D Bitmap shader within a shader network or linking to a parameter (e.g. skydome_light.color).
The Bitmap shader is translated to an Arnold image shader using the given File as the file name. You can also select the Alpha Channels layerset to read the alpha channel from the image. Other layer sets or any other parameters on the Shader tab (Sampling, Exposure, etc.) are not supported.
You can also define animated textures using the Bitmap shader's Animation tab. All parameters (Mode, Timing, etc.) are supported.