Chern character
= Chern character
{c}
{title2=$\operatorname{ch}:K^0(X)\to H^{\mathrm{ev}}(X;\mathbb Q)$}
{wiki}
If the formal Chern roots of $E$ are $x_1,\ldots,x_r$, then
$$
\operatorname{ch}(E)=\sum_{i=1}^r e^{x_i}.
$$
It extends to virtual bundles and is a ring homomorphism because direct sum joins root lists while tensor product replaces them by all sums $x_i+y_j$.