I am no expert in equivariant homotopy theory. Let's say, I am planing to give a talk on homotopy fixed points and orbits. My audience will be graduate students who are doing algebraic topology or others who have fair knowledge of basic algebraic topology.

I want to give lot of computational examples of fairly basic but illuminating examples homotopy orbits and homotopy fixed points and illustrate that

1. Homotopy orbits or fixed points differ from ordinary fixed points and ordinary orbits.
2. Examples two $G$-homotopy equivalent spaces, where the $G$-fixed points of respective spaces are not homotopic or the $G$-orbits of respective spaces are not homotopic.

However, I want to avoid examples involving spectra.

Please help me in creating a substantial list of examples/counterexamples/results (of any kind) related to homotopy fixed points and orbits that is suitable for an introductory/motivational talk. References will also be appreciated.

I am no expert in equivariant homotopy theory. Let's say, I am planing to give a talk on homotopy fixed points and orbits. My audience will be graduate students who are doing algebraic topology or others who have fair knowledge of basic algebraic topology.

I want to give lot of computational examples of fairly basic but illuminating examples homotopy orbits and homotopy fixed points and illustrate that

1. Homotopy orbits or fixed points differ from ordinary fixed points and ordinary orbits.
2. Examples two homotopy equivalent spaces, where the $G$-fixed points of respective spaces are not homotopic or the $G$-orbits of respective spaces are not homotopic.

However, I want to avoid examples involving spectra.

Please help me in creating a substantial list of examples/counterexamples/results (of any kind) related to homotopy fixed points and orbits that is suitable for an introductory/motivational talk. References will also be appreciated.

I am no expert in equivariant homotopy theory. Let's say, I am planing to give a talk on homotopy fixed points and orbits. My audience will be graduate students who are doing algebraic topology or others who have fair knowledge of basic algebraic topology.

I want to give lot of computational examples of fairly basic but illuminating examples homotopy orbits and homotopy fixed points and illustrate that

1. Homotopy orbits or fixed points differ from ordinary fixed points and ordinary orbits.
2. Examples two $G$-homotopy equivalent spaces, where the $G$-fixed points of respective spaces are not homotopic or the $G$-orbits of respective spaces are not homotopic.

However, I want to avoid examples involving spectra.

Please help me in creating a substantial list of examples/counterexamples/results (of any kind) related to homotopy fixed points and orbits that is suitable to give an introductory/motivational talk. References will also be appreciated.

I am no expert in equivariant homotopy theory. Let's say, I am planing to give a talk on homotopy fixed points and orbits. My audience will be graduate students who are doing algebraic topology or others who have fair knowledge of basic algebraic topology.

I want to give lot of computational examples of fairly basic but illuminating examples homotopy orbits and homotopy fixed points and illustrate that

1. Homotopy orbits or fixed points differ from ordinary fixed points and ordinary orbits.
2. Examples two $G$-homotopy equivalent spaces, where the $G$-fixed points of respective spaces are not homotopic or the $G$-orbits of respective spaces are not homotopic.

However, I want to avoid examples involving spectra.

Please help me in creating a substantial list of examples/counterexamples/results (of any kind) related to homotopy fixed points and orbits that is suitable for an introductory/motivational talk. References will also be appreciated.