You Rock Guitar

I have a YRG and use it to trigger software synths via midi. I'm having a hard time understanding your routing. You say you can "hear it on the monitors but can't get it to input to the audio channel". Does that mean that the synth is being triggered but you can't figure out how to record it?

I suggest you record the midi data on the midi track that is assigned to the YRG, then freeze the synth that is being triggered by the YRG.

I'm thinking (from my understanding of your Q) that you need to insert a Midi track (instead of an audio track) with the desired synth as your output to record.   

Bentley is correct, and this is one of the less intuitive things about Sonar.

So, on the MIDI track, in the Track view of the Inspector, you set the outputs to the correct MIDI port and channel.  I think you already have that figured out OK.

On the audio track, which is what you actually hear, at the bottom of Inspector in track view, made sure the audio inputs are whatever you have the synth plugged into in your audio interface.  (For me, for example, I might pick V-Studio Stereo 3-4, or something like that.  Yours choices will say something different.)  for the Output, most people would select Master if they have a master bus set up.  (You could also have your output set to whatever your main audio output is. I personally choose Master so the master fader on my console and in Sonar will control the overall mix.)
 
Unlike a virtual instrument, the MIDI track and audio track are not connected to each other in any way except by what you choose in the inputs of the audio track.  Example: I sometimes have one audio track fed by stereo inputs in my interface playing several sounds coming out of a synth on different MIDI channels; that is, multiple MIDI tracks are feeding one audio track.  I use this just for listening while I am arranging.  When I am ready to make a record, I solo one MIDI track at a time and record it.  I won't bog you down with details here, but if you want me to explain more, I will.

Warning: I am experiencing a bug that messes up the input settings on audio tracks and I have to go back, check them, and reset them from time to time.  I sincerely hope that is unique to my system and will not give you any grief.  The warning here is that anytime you can't hear something, a good first step is to check the input settings on your audio tracks.
 
Another example: if you open up some General MIDI type file you downloaded, it won't make any sound until you create an audio track and set the inputs on the audio track to wherever you synth is plugged in.  If your synth is plugged into #1 on your audio interface, the input drop down for that track should have that as a choice.

Best of luck and let us know how it goes.

Plug the guitar output into your soundcard and you can record it on an audio track. 

Do take the time to read through the manual and make all the little tweaks so it works with your playing style. For a lot of people it works fine "out of the box" with default settings, but a little tweakage can really make a difference in terms of accuracy and playability.