What's the best way to fix carbon to titanium? I'm building (experimenting if you wish) something out of the old bike parts and I need to fix two parts together one titanium and carbon.

Basically the parts are two tubes one made of carbon of a lower diameter and one made of titanium. So the carbon tube goes inside the titanium tube and I need to find a way to fix it inside for good. I guess it should be some kind of a hardcore gluing.

If anyone have any experience or suggestions please share. Thank you!
There are many companies today producing "lugged" frames out of aluminum/steel/titanium with carbon fiber tubes.  Seven Cycles is one example, but there are others.  Additionally, some people are independently making carbon frames with lugs that have been created using 3D printer madness.  Reading various forums and the last link, 3M, Loctite and West System all make epoxies that would work for such an application.  Your best bet would likely be to contact the company and have them recommend which product would be appropriate.

All of this assumes that you are trying to lug a piece that will be under compression.  Lugged bicycle frames work because the triangle largely experiences compression forces which actually force the tubes into the lugs.  Forces acting to pull the tube out of the lug are more rare and the epoxy acts mainly to hold the setup together and isn't as "structural" (bad use of the term) as the lugs or tubes.  If this is not what you are trying to accomplish, you may look for a different solution since gluing/epoxying together two pieces that will be under tension will rely on the strength of the epoxy to hold them together and likely not be appropriate for the forces generated cycling.