From the tests we have done here - you are only able to directly export a static (non-animated) object from C4D using Collada 1.4.
This model can have a texture - but it has to be applied in the self-illumination/luminance channel. This is important because lights do not export correctly - if you don't put your texture in the self-illumination channel you model will appear to be black (because it is un-lit). Use of diffuse maps in the luminance channel can circumvent the lighting setback.
The way the animation is encoded in files exported by C4D seems to be in an unrecognised format - this is because Cinema 4D is using the standard Collada 1.4 exporter - the Open Collada group has not yet released an OpenCollda plugin for Cinema 4D.
Cinema4D will export models and texture maps using Collada 1.4, but using Collada 1.5 will not export texture map.
Here is a screenshot of the Cinema 4D export settings for Collada 1.4:
In an ideal world, users are strongly recommended to use the OpenCollada DAE exporter where possible - this can be downloaded for 3ds Max and Maya, but a plug-in hasn't been released for Cinema 4D yet.
AutoDesk FBX Converter
If you are therefore interested in using an unanimated object, with no lights in the scene then our best advice would be to export your object & lights as an FBX file. And use the Autodesk FBX converter to change the FBX into a Collada DAE. This seems to work with Cinema 4D files, but we haven't thoroughly tested this method - so please let us know if it does work for you or not.
The alternative is to export from Cinema 4D as an FBX - with a rig, animation and lights. You can then import it into Blender, and from there you can export as a DAE which is compatible with Aurasma.
You can find a more detailed article on use of Blender here
Here is a work-flow that outlines the 2 possible processes you can follow, depending on whether you want to use animated rigged models in Aurasma or not: