There exists a Quillen equivalence between $HRModSpectra$ (homotopy category of ring spectra over Eilenberg-MacLane spectra EM(R), where R is a commutative ring, with stable model structure ) and $HoCh$ (homotopy category of unbounded chain complexes of R-modules ).

I was wondering what are the Quillen functors which give the above Quillen equivalence.

One can start with an unbounded chain complex $X$ and apply Dold-Kan functor $\Gamma$ to chain complex $X_{\geq 0}$ to get a simplicial abelian group $\Gamma(X_{\geq 0})$, and then consider $\Gamma(X[-n]_{\geq0})$ (shifting $X$ to the left by n places , truncating and then applying $\Gamma$). This way one gets an $\Omega$- spectra $Y$ ={$\Gamma(X_{\geq 0})$, $\Gamma(X[-1]_{\geq0})$ , ...}.

How does then one proceed to prove that $Y$ is a symmetric spectra.