Let $X$ be a smooth proper $k$-scheme with an endomorphism $X\overset{g}\to{\rightarrow}X$ such that the graph of $g$ intersects the diagonal in $X\times X$ transversely. The holomorphic Atiyah-Bott fixed-point formula says that for a lax $g$-equivariant perfect sheaf $(E,t)$, i.e., a sheaf ${E\in{\rm QCoh}(X)^{\rm perf}}$ equipped with a map $E\overset{t}\to{\rightarrow}g_*E$, one has $$ \ssf{Tr}_{{\rm Vect}_k} \left(\Gamma(X,E) \overset{\Gamma(X,t)}\to{\longrightarrow}\Gamma(X,E)\right) = {\sum_{x=g(x)}} \frac{\ssf{Tr}_{{\rm Vect}_k} \left(E_x \simeq E_{g(x)}\overset{t_x}\to{\longrightarrow}E_x\right)}{\det(1-d_x g)}, $$ where $\Bbb{T}_{X,x}\overset{d_xg}\to{\longrightarrow}\Bbb{T}_{X,g(x)}\simeq\Bbb{T}_{X,x}$ is the induced map on tangent spaces. \par Let $X\rightarrow Y$ be an equivariant morphism between smooth proper schemes, with $g_X$ and $g_Y$ acting on $X$ and $Y$, respectively, such that reduced fixed loci $\overline{X^{g_X}}$ and $\overline{Y^{g_Y}}$ are smooth and the induced morphisms on conormal bundles $1-(g_X^*)_{|\Cal{N}_{g_X}^\vee}$ and ${1 - (g_Y^*)_{|\Cal{N}_{g_Y}^\vee}}$ are invertible. Equivariant Grothendieck-Riemann-Roch says that for a lax $g_X$-equivariant perfect sheaf $E$ on $X$, one has $$ (\overline{f^g})_* \left({\rm ch}(E,t)\frac{{\rm td}_{\overline{X^{g_X}}}}{e_{g_X}}\right) ={\rm ch}(f_*(E,t))\frac{{\rm td}_{\overline{Y^{g_Y}}}}{e_{g_Y}}\in{\bigoplus_p}H^{p,p}(\overline{Y^{g_Y}}), $$ involving the equivariant Chern character, Todd classes, and equivariant Euler classes, where $\overline{X^{g_X}}\overset{\overline{f^g}}\to{\longrightarrow} \overline{Y^{g_Y}}$ is the induced map on reduced fixed loci. \par The authors use the formalism of traces in higher categories to prove a common generalization of the two theorems above. The proof relies on the interplay between self@-dualities of quasi- and ind-coherent sheaves on $X$ and the formal deformation theory of Gaitsgory and Rozenblyum. That is, the authors give a description of the Todd class in terms of the difference of two formal group structures on the derived loop scheme $\Cal{L}X$. The equivariant case is reduced to a non-equivariant scenario by a variant of the Atiyah-Bott localization theorem.