Unlink the projects you have worked in and your employment history.

Make two sections in your résumé:

• Projects, This should include side projects and everything that you consider relevant evidences to prove your qualifications.
  List technical details, e.g. development tools and platforms you have used (and supposedly you're familiar with).
  Indicate your role and the most interesting activities you have participated in, regarding each project (expos, contests, whatever).
  It does not matter who's the project owner. You may simply skip the employer's company name, but be ready to provide with references when asked.

My personal preference is to have this section just after the contact info, as it seems to be the most important to me.

• Career, where all employers and formal positions (employment history) is recorded. You probably have this already.

Further reading from Workspace.SE:

• How should I list the employer for contract work on my resume?How should I list the employer for contract work on my resume?
• Incorporating off-job technical qualifications on resumeIncorporating off-job technical qualifications on resume
• Handling a Gap in Your RésuméHandling a Gap in Your Résumé